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Question

In the following figure;

IA and IB are bisectors of  CABandCBArepsectively.

CP is parallel to IA and CQ is parallel to IB. 


Solution

Since IA || CP and CA is a transversal

 \(\angle  CAI =  \(\angle  PCA                [Alternate angles]

Also, IA || CP and AP is a transversal

 IAB=APC           [Corresponding angles]

But CAI=IAB          [Given]

PCA=APC

AC = AP

Similarly,

BC = BQ

Now,

PQ = AP + AB + BQ

= AC + AB + BC

= Perimeter of triangle ABC


Mathematics
Concise Mathematics
Standard IX

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