In triangle ABC, ∠ABC=90∘ and P is a point on AC such that ∠PCB=∠PBC, then PA = __
A
PB
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B
PC
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C
2 PB
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D
2 PC
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Solution
The correct option is A PB Let angle ∠PCB=∠PBC=x In the right angled triangle, ∠ABC=90∘ ∠ACB=x
∠BAC=180∘−(90∘+x) =90∘−x .. (i) And, ∠ABP=∠ABC−∠PBC =90∘−x ..( ii) From (i) and (ii), we get ∠BAC=∠ABP PA = PB [Sides opposite to equal angles are always equal]