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Question
In a quadrilateral PQRS, if the bisectors of ∠ SPQ and ∠ PQR meet at O, prove that O is equidistant from PS and QR.
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Solution
OP bisects ∠ SPQ and OQ bisects ∠ PQR.
Draw OM perpendirular to RQ and OL perpendirular to SP
Now in Δ OQM and Δ OLP
∠ OLP = ∠ OMQ
∠ OPL = ∠OQM
OP= OQ
Therefore, Δ OQM and Δ OLP are oongruent.
Hence, OL = OM
O is equidistant from PS and QR. Proved.
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