Q. 35.0( 28 Votes )

Prove that the center of a circle touching two intersecting lines lies on the angle bisector of the lines.

Answer :


Let PR and PQ are two intersecting lines [intersects on point P] touching the circle with center O and we joined OR, OQ and OP.


To Prove : Center O lies on the angle bisector of PR and PQ i.e. OP is the angle bisector of RPQ


Proof :


Clearly, PQ and PQ are tangents to the circle with a common external point P.


In POR and POQ


OR = OQ [radii of same circle]


OP =OP [Common]


PR = PQ [Tangents drawn from an external point to a circle are equal ]


POR POQ [ By Side Side Side criterion ]


RPO = OPQ [ Corresponding parts of congruent triangles are equal ]


This implies that OP is the angle bisector of RPQ .


Hence Proved .


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on Circles32 mins
Quiz | Imp. Qs. on CircleQuiz | Imp. Qs. on CircleQuiz | Imp. Qs. on Circle35 mins
Important Questions on CirclesImportant Questions on CirclesImportant Questions on Circles46 mins
Quiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on Circles37 mins
RD Sharma |  Important Questions on CirclesRD Sharma |  Important Questions on CirclesRD Sharma | Important Questions on Circles36 mins
Short Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of Triangle43 mins
Tangent from an External PointTangent from an External PointTangent from an External Point54 mins
RD Sharma | Most Important Questions of CirclesRD Sharma | Most Important Questions of CirclesRD Sharma | Most Important Questions of Circles35 mins
Smart Revision | CirclesSmart Revision | CirclesSmart Revision | Circles44 mins
RD Sharma | Imp Qs Discussion on Area Related With CirclesRD Sharma | Imp Qs Discussion on Area Related With CirclesRD Sharma | Imp Qs Discussion on Area Related With Circles41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses