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Question
Angle BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.
Solution
In ΔABC,
AC = AB ...(Given)
`=>` ∠ABC = ∠ACB ...(Angles opposite equal sides are equal)
In ΔPRC and ΔPQB,
∠ABC = ∠ACB
∠PRC = ∠PQB ...(Both are right angles)
`=>` ΔPRC ∼ ΔPQB ...(AA criterion for similarity)
`=> (PR)/(PQ) = (RC)/(QB) = (PC)/(PB)`
`=> (PR)/(PQ) = (PC)/(PB)`
`=> 9/15 = 12/(PB)`
`=>` PB = 20 cm
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