Visual Geometry - · PDF fileVisual Geometry . To join Classroom or online program call...

To join Classroom or online program call 09820500380 or see details cetking.com

Visual Geometry

To join Classroom or online program call 09820500380 or see details cetking.com To join Classroom or online program call 09820500380 or see details cetking.com

1 of 12 workshop series

Quant cutoff clearing: 1. Visual Geometry 2. Vedic Numbers 3. Equations Polynomials 4. Dirty (Modern) Quant 5. Arithmetic 6. DI Without Pen

Verbal cutoff clearing: 1. RC in half time 2. Grammar/Sentence Cor 3. Vocab & FIBs 4. Paragraph Comp & Jum 5. Critical Reasoning 6. Logical Reasoning

Visual Geometry


Homework before workshop

Try these questions without using pen!


Scope • Angles • Circles • Triangles – Theorems • Triangles – Similar/Cong • Mensuration – Areas • Mensuration – Volume • Trigonometry Geometry • Coordinate Geometry


Importance


Geometry • Angles • Circles • Triangles – Theorems • Triangles – Similar/Cong • Mensuration – Areas • Mensuration – Volume • Trigonometry Geometry • Coordinate Geometry

Visual Geometry

• Angles • Side • Area


1.Uniform Figures

2.Triple Delight

3.Draw Lines

4.Scale drawing

5.Angular

6.Drawing to scale

7.Trigonometry

8.Areas

9.Volumes

10.Circles in C

Visual Geometry


AB ⊥ BC, BD ⊥ AC and CE bisects ∠C, ∠A = 30°. Then what is ∠CED?

a. 30° b. 60° c. 45° d. 65°


Find the area bigger circle A? 1. 4∏ 2. 6∏ 3. 8∏ 4. 3∏

A


Total circumference of smaller circles If the diameter of the biggest circle is 20m 1. 40∏ 2. 20∏ 3. 18∏ 4. 30∏


Ratio of shaded to unshaded area If the diameter of the biggest circle is 20m 1. 2:1 2. 1:1 3. 1:3 4. 2:3


In the given figure, AB is diameter of the circle and points C and D are on the circumference such that ∠CAD = 30° and ∠CBA = 70°. What is the measure of ∠ACD? a. 40° b. 50° c. 30° d. 90°


VIRTUAL POSITIONING


a)25 b)35 c)45 d)55


PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. Then the ratio of area of the circle to the area of the square is


In ΔABC, ∠B is a right angle, AC = 6

cm, and D is the mid-point of AC. The length of BD is


From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion? a. 1 : 3 b. 4 : 1 c. 3 : 1 d. 4 : 3


Given: AC = BD AD = 15 AE = 9 Find the area of trapezium? 1. 108 2. 612 3. 112 4. 152


Circle in square Finding Radius Finding Area


Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps: the original square of side a is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is:

1 : 1 2. \/2 : 1

3. n(4 - n)/(4n - n) 4. (4n -n)/n(4 - n)

CAT2004


Circle of radius 2 is placed against a right angle. Another smaller circle is also placed as shown. What is the radius of the smaller circle? a. 3-2√2 b. 4-2√2 c. 7-4√2 d. 6-4√2


The figure shows the rectangle ABCD with a semicircle and a circle inscribed inside in it as shown. What is the ratio of the area of the circle to that of the semicircle?


a) 20 b) 30 c) 50 d) 60

Find ADE angle


The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of ΔABC. a. 60 sq. cm b. 30 sq. cm c. 40 sq. cm d. 52 sq. cm


In ACD, AD = AC and ∠C = 2 ∠E. The distance between parallel lines AB and CD is h. Then: I. Area of parallelogram ABCD II. Area of ADE.

Mark (a) if I > II. Mark (b) if I < II. Mark (c) if I = II. Mark (d) None


a. 12 cm b. 15 cm c. 8 cm d. 11c m


What is the length of rectangle ABCD? I. Area of the rectangle is 48 square units. II. Length of the diagonal is 10 units.

a. if I alone. b. if II, alone. c. if both statement d. None


The length of a ladder is exactly equal to the height of the wall it is learning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then the height of the wall is a. 12 m b. 15 m c. 18 m d. 11 m


In ΔABC, ∠B is a right angle, AC = 6

cm, and D is the mid-point of AC. The length of BD is

In a right angled triangle median is equal to half of the hypotenuse


In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC. a. 4√2 b. 5 c. 3.5 d. None of these


QR is parallel to ST. What is the length of PR? a) 4.8 b) 3.2 c) 5.7 d) 4.2


k1, k2, k3 are parallel lines. AD = 2 cm, BE = 8 cm and CF = 32 cm. I. (AB)×(EF) II. (BC)×(DE)

Mark (a) if I > II. Mark (b) if I < II. Mark (c) if I = II. Mark (d) None


In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of Δ CBE to that of Δ ADE? a. 1 : 4 b. 1 : 2 c. 1 : 3 d. Data insufficient


In Δ ABC, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of Δ ABC is 20 sq. units, find the area of Δ PQR. a. 10 sq. units b. 5√3 sq. units c. 5 sq. units d. None of these


Find the area of the shaded triangle to that of the complete triangle

a) 1/8 b) 1/32 c) 1/16 d) Cannot be det


What is the length of rectangle ABCD? I. Area of the rectangle is 48 square units. II. Length of the diagonal is 10 units.

a. if I alone. b. if II, alone. c. if both statement d. None


Find the height of the string d? a) 300√3 b) 600 c) 300 d) 400√3 e) 200√3

d


Find the distance between the posts d? a) 300√3 b) 600 c) 300 d) None of th.


In the figure below, What is the ratio of the area of the sector to that of the circle

a) 1/12 b) 1/6

c) 1/24 d) 1/2


In the figure below, What is the ratio of the area of the shaded region to that of the rectangle with Length 20 and breath 10.

a) 1/2 b) 1/6

c) 1/4 d) 1/12

Cut and adjust



a) 1/2 b) 1/6

c) 1/4 d) 1/8



a) 1/2 b) 1/6

c) 1/4 d) 1/12



a) 1/2 b) 5/6

c) 3/4 d) 3/8


In the figure below, ABCDEF is a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF? a) 1/12 b) 1/6

c) 1/24 d) 1/2


In the figure below, ABCDEF is a regular hexagon and angle AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? CAT 2003

a) 1/12 b) 1/6

c) 1/24 d) 1/18


In the figure below, ABCDEF is a regular hexagon. Find the area of shaded region if the area of hexagon is 600?

a) 200 b) 600

c) 300 d) 180


In the figure below, Find the area

of shaded region I and II if the side of the square is 20m?

a) 200 b) 60

c) 300 d) 50


In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of Δ CBE to that of Δ ADE? a. 1 : 4 b. 1 : 2 c. 1 : 3 d. Data insufficient


Coordinate


Equation of line joining two points

Find the equation of the line passing through (-1,-2) & (-5,2)

(a) 2x + y = 3

(b) 3x - 2y + 7 = 0

(c) x + y + 3 = 0

(d) None of these

Two Point Form:

(y + 2)/(-2-2) = (x + 1)/(-1+5) 4(y + 2) = -4 (x + 1) y + 2 = -x -1 x + y = -3 Option (c)


Equation of line joining two points

Find the equation of the line passing through (2,-4) & (-3,2)

(a) 2x + y = 3

(b) 6x - 5y + 7 = 0

(c) 5x + 6y + 3 = 0

(d) None of these

Two Point Form:

(y - 2)/(2+4) = (x + 3)/(-3 - 2) -5(y - 2) = 6(x + 3) -5y + 10 = 6x +18 6x + 5y = -8 Option (d)


Equation using slope and point

Find the equation of line passing through point (2,-3) having slope 5/4.

(a) 4x - 5y = 20

(b) 3x – 2y = 5

(c) 5x - 4y = 22

(d) None of these

(y - y1) = m (x-x1) (y + 3) = 5/4 (x - 2) 4y + 12 = 5x -10 5x - 4y = 22 Option (c) Note: Sometimes angle will be given. Slope can be

found as tanѲ


Point of intersection of two lines

Point of intersection of 2x + y = 4 and x - y + 1= 0

a) (3, 1)

b) (1, 2)

c) (3, 2)

d) (1, 4) Solution of two equations is the point of intersection 3x = 3 x=1 2 + y = 4 y = 2 Solution: (1 ,2)


Distance between points

Find the distance between (7, 5) & (4, 1)

a) 5

b) 5 √2

c) 7 √3

d) 10


Distance between points

Find the distance between

(4, 2) & (6, 6)

a) 5

b)4.47

c) 4.14

d)4.65


Equation of parallel

Find the equation of the line passing through point (2,7) and parallel to 2x + 3y + 8= 0

a) 5x - 2y = 17

b) 2x + 3y = 25

c) 2x + 3y = -4

d) 4x + 6y = -16

Slope of options (b), (c) and (d) match the condition of parallelism Only option (b) satisfies (2,7)


Equation of perpendicular

Find the equation of the line passing through point (2,7) and perpendicular to 2x + 3y + 8= 0

a) 5x – 2y = 17

b) 3x + 2y = 20

c) 3x – 2y = -4

d) 6x – 4y = -16

Slope of options (c) and (d) match the condition of perpendicularity Only option (d) satisfies (2,7)


Equation of perpendicular

Find the equation of the line passing through point (-4,-9) and perpendicular to 3x - 5y + 8= 0

a) 5x – 2y = 17

b) 10x + 6y = 20

c) 3x – y = -4

d) -5x – 3y = 47

Slope of options (c) and (d) match the condition of perpendicularity Only option (d) satisfies (2,7)


Geometry • Angles • Circles • Triangles – Theorems • Triangles – Similar/Cong • Mensuration – Areas • Mensuration – Volume • Trigonometry Geometry • Coordinate Geometry

Visual Geometry

• Angles • Side • Area


1.Uniform Figures

2.Triple Delight

3.Draw Lines

4.Scale drawing

5.Angular

6.Drawing to scale

7.Trigonometry

8.Areas

9.Volumes

10.Cir in Cir

Visual Geometry


To join Classroom or online

program

call 09820500380 or see details cetking.com

Visual Geometry - · PDF fileVisual Geometry . To join Classroom or online program call...

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