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in cyclic quadilaater opposite sides sum is 180
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GIVEN: AB=AC
PQ||BC
REQUIRED TO PROVE: BCPQ is cyclic
PROOF: In triangle ABC
AB=AC (given)
therefore anglePBC= angle QBC------(1)
PQ||BC
therefore angle QPB + anglePBC = 180°
angle QPB + angle QBC = 180° [from (1)]
we can observe that opposite angles are supplementary
therefore BCPQ is cyclic
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