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ICSE Class X Math 2016 Paper

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In the given figure PQRSP Q R S is a cyclic quadrilateral PQP Q and SRS R produced meet at TT.
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Question : 24 of 57
Marks: +1, -0
Prove △TPS∼△TRQ\triangle TPS \sim \triangle TRQ.
Solution:  
In â–³\triangle TPS and â–³\triangle TRQ
  ∠PST=∠RQT\;\angle PST = \angle RQT
  ∠SPQ=∠QRT\;\angle SPQ = \angle QRT
[∵[ \because exterior angle of cyclic quadrilateral is equal to the interior opposite angle]
∠T  =∠T     (common)   \angle T \; = \angle T \;\; \text{ (common) } \;
∴    △TPS  ∼△TRQ  (   By AA)   \therefore \;\; \triangle TPS \;\sim \triangle TRQ \; ( \; \text{ By AA) } \;
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