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Prove that ABCD given in the figure is cyclicDraw figure and mark PQ If ∠BAP = x then what is ∠BQP? Find ∠PQD Find ∠PDC? Why? What is ∠A + ∠C?

Answer»

i. Quadrilateral ABPQ is cyclic If ∠A = x, then ∠BQP = 180 – x

If ∠B = y, then ∠APQ = 180 – y 

Quadrilateral PQCD is cyclic, SO 

∠QCD = 180 – x (∠DPQ = x ) 

∠PDC = 180 – x (∠PQC = y) 

∴ ABCD is a cyclic quadrilateral.



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