4.12: TANGENTSB. Concepts And Characteristics Of TangentsC. Concepts And Characteristics Of TangentsDetermining The Tangent Point Between A Straight Line And A CircleDetermining The Tangent Points Of Two Straight LinesDetermining A Tangent Point Between Two Circles In Touch Internally Or ExternallyDetermining The Tangent Points Between A Circle And Two Other CirclesDetermining Tangent Points Between A Straight Line And Two Circles In Touch ExternallyDetermining Tangent Points Between A Line And Two Circles In Touch InternallyWhen The Point Is On The CircumferenceWhen The Points Is Outside Of The CircleConstructing A Circle Tangent To A Straight Line Given Radius of CircleA. Concepts And Characteristics Of TangentsConstructing A Circle In Tangent To Two Straight Lines Given Radius Of CircleConstructing A Circle Touching Externally With Another CircleConstructing A Circle Touching Internally With Another CircleConstructing An Arc In Touching Internally To Two Other CircleConstructing An Arc In Touching Externally With Two Other CirclesConstructing A Circle In Touch With Another Circle Internally Through A Given PointConstructing A Circle In Touch To Another Circle Through A Given Point

CONCEPTS AND CHARACTERISTICS OF TANGENTSA circle in touch with a lineRadius ( R )Normal line.Tangent point ( P ).Straight line

CONCEPTS AND CHARACTERISTICS OF TANGENTSTangent point ( T ).Another circle internally.A circle in touch with another circle internally.

CONCEPTS AND CHARACTERISTICS OF TANGENTSTangent point ( T ).Another circle externally.A circle in touch with another circle externally.

DETERMINING THE TANGENT POINT BETWEEN A STRAIGHT LINE AND A CIRCLE Given a circle in touch with a straight line. With the centre at O, draw two arcs intersecting the straight line at A and B. With centres at A and B, draw arcs intersecting at C. Draw the line OC. T is the tangent point.

DETERMINING THE TANGENT POINTS OF TWO STRAIGHT LINES Given a circle in touch with two straight lines. Draw a bisector line through the circle centre O. Draw perpendicular lines from O to AB and BC intersecting at T and U. T and U are the tangent point.

DETERMINING A TANGENT POINT BETWEEN TWO CIRCLES IN TOUCH INTERNALLY OR EXTERNALLY Given two circles. Given the two circles are in touch externally. Draw bisector lines AB and CD, intersecting at P. Repeat above step for the smaller circle so as to intersect at Q.Draw the line PQ. T is the tangent point.

DETERMINING THE TANGENT POINTS BETWEEN A CIRCLE AND TWO OTHER CIRCLESGiven a circle with radius R, a circle with radius r and a radius x.With centres at A and B, draw an arc with the radius (R + x) and an arc with the radius (r + x) intersecting at C.With the centre at C, draw a circle with the radius x. T and U are the tangent points.Draw the lines AC and BC intersecting at T and U.UC

DETERMINING TANGENT POINTS BETWEEN A STRAIGHT LINE AND TWO CIRCLES IN TOUCH EXTERNALLYGiven circles with radius R and r.Construct a semicircle with diameter AB and centred at A, construct a circle with radius (R - r) so as to intersect at C.Draw line TU. T and U are the tangent points.Extend the line AC to intersect at T. Draw a parallel line through B to intersect at U.r

DETERMINING TANGENT POINTS BETWEEN A LINE AND TWO CIRCLES IN TOUCH INTERNALLYGiven circles with radius R and r.Construct a semicircle with diameter AB. Centred at A, construct a circle with radius (R + r) intersecting at C.Draw a line AC intersecting at T. Draw parallel line through B so as to intersect at U.Draw line TU. T and U are the tangent points.

WHEN THE POINT IS ON THE CIRCUMFERENCEGiven a circles and point T.Draw line OT. Centred at T, draw an arc with radius r intersecting at P and Q.Draw arcs centred at P and Q intersecting at S.Draw line ST. Line ST is the tangent.r

WHEN THE POINTS IS OUTSIDE OF THE CIRCLEGiven a point P outside of a circle.Draw line OP and bisect it.Construct a semicircle to intersect at R. Draw normal line OR.Draw line PR. PR is the tangent line.

CONSTRUCTING A CIRCLE TANGENT TO A STRAIGHT LINE GIVEN RADIUS OF CIRCLEGiven a line and radius of a circle R.Mark the tangent point T. Centred at T, construct a perpendicular line.Centred at T, draw an arc with radius R intersecting at O.Centred at O, draw a circle through T.R

CONSTRUCTING A CIRCLE IN TANGENT TO TWO STRAIGHT LINES GIVEN RADIUS OF CIRCLEGiven two lines and radius R.Bisect the angle ABC.Construct a perpendicular line at A and construct a parallel line with distance of radius R intersecting at O.Draw perpendicular lines OP and OQ and draw a circle through P and Q.

CONSTRUCTING A CIRCLE TOUCHING EXTERNALLY WITH ANOTHER CIRCLEGiven a circle with radius R, a radius r and tangent point T.Draw line PT.Centred at P, construct arc (R + r) intersecting at O.Centred at O, construct a circle with radius r through T.

CONSTRUCTING A CIRCLE TOUCHING INTERNALLY WITH ANOTHER CIRCLEGiven a circle with radius R, radius r and tangent point T.Draw straight line OT.Centred at O, draw arc (R r) intersecting at Q.Centred at Q, construct a circle with radius r through T.

CONSTRUCTING AN ARC IN TOUCHING INTERNALLY TO TWO OTHER CIRCLEGiven a circle with radius R, radius r and a radius J.Centred at A, construct an arc (J r). Centred at B, construct an arc (J r) intersecting at P.Draw straight lines PA and PB intersecting at S and T.Centred at P, construct an arc or a circle with radius J intersecting at S and T.

CONSTRUCTING AN ARC IN TOUCHING EXTERNALLY WITH TWO OTHER CIRCLESGiven circle with radius R, radius r and a radius J.Centred at A, construct an arc (R + J). Centred at B, construct an arc (r + J) intersecting at P.Draw lines PA and PB intersecting at S and T.Centred at P, construct an arc or a circle with radius J through S and T.

CONSTRUCTING A CIRCLE IN TOUCH WITH ANOTHER CIRCLE INTERNALLY THROUGH A GIVEN POINT Given a circle, tangent point R and point P.Draw line PR and bisect it.Draw straight lines RO to intersect at S.Centred at S, construct an arc through P and R.

CONSTRUCTING A CIRCLE IN TOUCH TO ANOTHER CIRCLE THROUGH A GIVEN POINT Given a circle and point P.Draw perpendicular line PR. Draw line OA parallel to PR.Draw line AP intersecting at K. Draw line OK intersecting at S.Centred at S, construct an arc through P and K.