Question
ABCD is a cyclic quadrilateral in which AB =16.5 cm. BC
= x cm. CD= 11 cm. AD 19.8 cm, and BD is bisected by AC at O. What is the value of x?Solution
From the following figure, => ∠ACD = ∠ABD (angle made by a chord in same segment are equal) => ∠BDC = ∠BAC (angle made by a chord in same segment are equal) So, Δ AOB ~ Δ DOC by AA => OB/OC = 16.5/11 => OB = OD (given) => OD/OC = 16.5/11 ------ (i) As we know, => Δ ADO ~ Δ BCO => OD/OC = AD/BC => OD/OC = 19.8/x ------ (ii) Solving equation (i) and (ii) we get, => 19.8/x = 16.5/11 => x = (11 × 19.8)/16.5 => x = 13.2 cm
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