Name Gender

Address Phone E-mail

Designers Caswita M Lampung (0721)267529 Caswita@unila.ac.id

Directors Herawati F Jakarta (021) 7414952 Hera_0912@yahoo.com

Teacher Mery F Jakarta 081319204959 Merynoviyanti@yahoo.com

Prod. Of coursware

Isa &

Abdul kadir

M

M

Semarang

Malang

081326527310 Isaakhlis@gmail.com

Abdkadir@umm.ac.id

Prod. Of CD room

Wayan M Bali (0362)31955 Batungsel@yahoo.com

Target state :

Students can be able to draw common tangent by using a compass and a ruler as well the length of it

Student Objective

1. identifying the position of two circles and re-cognizing the common tangent of them (if it exists)

2. drawing and calculating the length of common tangents of circles

3. solving problems involving tangents

4. explaining tangents kites

Content analysis

Keypoint : common tangent of circles Topic student difficult to understand: drawing

tangent of circles by compass and determine the length of tangent

Relationship of content to be learnt and the other content (circles, line, phytagoras theorm)

Relationship between different topics within the content area: position of the circles, drawing tangent by compass and determining length of tangent

Student analisis

Cognitive analysisDrawing and calculating length of tangent

Prior analisis: students know about lines, circles, Pythagoras theorm

skill of student: they can use compass and ruler

Procedure and teaching strategies

Direct learning Cooperative Learning

Description of teaching and learning processPhases Teaching

ActivitiesLearning Act Ass. alongside Use of ICT Time needed

Intro Teachers tell about the objective of learning

Student listen about the object

Teacher give a questions

Powerpoint 5

Main activities

Techers tach subject

Student solve problems in group and then present the result

Problems Powerpoint, compass

70

closing Techer give the summaries and homework

Student listen and ask questions

exercise powerpoint 15

8.2 Common tangent of circles

Objectives:

1. identifying the position of two circles and re-cognizing the common tangent of them (if it exists)

2. drawing and calculating the length of common tangents of circles

3. solving problems involving tangents

4. explaining tangents kites

The students are expected to be capable

The position of two circles

Given two circles centered at point M and N with radius R and r where R > r, respectively

Problem :

1. How many possibilities the position of two circles can be made ?

2. Determine the number of lines that touch each circle exactly at one point ?

The length of MN is less than (R - r)

Then the circle N is inside the circle M,

M

R N

r

M = N

Rr

On the Case M = N, the circles M and N are called concentric circles (the circles have a common center)

so thatthere is no line touching each circle exactly at one point

Case 1:

Case 2 : The length of MN is equal to (R – r).

so that there is only one line touching each circle exactly at one point so-called common tangent (of circles M and N)

M

RN

r

circle N touches inside the circle M exactly at one point,

Then the

Case 3 : The length of MN is equal to (R + r).

circle N touches outside the circle M exactly at one point,

Then the

so that there are three lines touching each circle exactly at one point

O

P

Q

The Line through O and perpendicular to line MN is called inner common tangent, the lines PQ and ST are called outer common tangent (of circles (M,R) and (N,r)

S

T

M

R

Nr

Work in Group :

Determine the number of common tangent of Circles (M ; R) and (N ; r) for the other cases, and show by pictures

Drawing common tangent of circles and determining the length of it

Given two circles centered M and N with radius R and r such that MN > R + r

Problem:

1. How to draw inner and outer common tangents ?

2. Determine the length of inner and outer common tangents ?

ProcedureDrawing inner common tangent

1. Draw circles (M ; R) and (N ; r) with MN > R+r

2. Draw a circle centered at M with radius of R+r

3. Draw a line passing points M and N, and then find mid-point O of it

4. Draw circle with center at O and radius OM, then it intersects circle (M ; R+r) at two points, namely P and Q

5. Draw lines NP and NQ, then they are tangent of circle (M ; R+r) ( Why ? )

6. Draw line through N downward and parallel to PM intersecting circle (N ; r) at S, then line ST paralel to NP is an inner common tangent

M

R

rN

O

P

Q

S

T

7. Similarly, the another inner common tangent UV will be found

U

V

The length of inner common tangent

means that distance of common point of tangent and one circle to that of tangent and another

Observe right-angled triangle NPM, then 22 )()( NPMNNP

Because ST // NP and NS // PT, then ST = NP so that the length of inner common tangent ST is equal to

22 )()( NPMN Similarly, the length of inner common tangent UV is equal to that of ST

Drawing outer common tangent

1. Draw circles (M ; R) and (N ; r) with MN > R+r

2. Draw a circle centered at M with radius of R-r

3. Draw a line passing points M and N, and then find mid-point of it, namely O

4. Draw circle with center at O and radius OM, then it intersects circle (M ; R-r) at two points, namely P and Q

5. Draw lines NP and NQ, then they are tangent of circle (M ; R-r) ( Why ? )

6. Draw line through N upward and parallel to PM intersecting circle (N ; r) at S, then line ST which is parallel to NP is an inner common tangent

M

R

rN

O

P

Q

S

T

U

V

7. Similarly, the another inner common tangent UV will be found

The length of inner common tangent

Observe right-angled triangle NPM, then

22 )()( NPMNNP Because ST // NP and NS // PT, then ST = NP so that the length of inner common tangent ST is equal to

22 )()( NPMN Similarly, the length of inner common tangent UV is equal to that of ST

Work in Group :

Draw common tangent of Circles (M ; R) and (N ; r) for the case MN = R+r, and determine the length of them