Circle with secant (REPOST)

AIEEE 2015 Discussion Forum › Co-ordinate Geometry questions › Circle with secant (REPOST)

AB is a secant which intersects a circle with centre O at the points C and D such that AC=BD. From A, B two tangents AR and BS are drawn to meet the circle at the points P and Q respectively( as given in the diagram). PQ joined intersects chord CD at T Prove that CT=TD

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Manish Shankar ·2012-07-25 06:07:56

compare traingles OAP and OBQ

and then compare triangles OAT and OBT

so construct the triangle and try it

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Abhirup Banerjee Sir, I have proved the triangles OAP and OBQ congruent.( by R-H-S congruency) But, if you observe you will not be able to establish congrency between OAT and OBT just by comparing them. It is required to prove certain other conditions to satisfy the congruency ( S-A-S, S-S-S, or R-H-S) I will be happy if you kindly help me with a formal and a complete proof. Thanks, Abhirup Banerjee
Upvote·0· Reply ·2012-07-27 10:34:06
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Circle with secant (REPOST)

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