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Question
The bisector of the equal angles of an isosceles triangle PQR meet at O. If PQ = PR, prove that PO bisects ∠P.
Sum
Solution
Join PO and produce to meet QR in S.
In ΔPQS and ΔPRS
PS = PS ...(common)
PQ = PR ...(given)
∠Q = ∠R
∴ ΔPQS ≅ ΔPRS
∴ ∠QPS = ∠RPS
Hence, PO bisects ∠P.
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