Question

Hello,
Please help me with the following :
Angle BAC of triangle ABC is obtuse and AB=AC. P is a point in bc such that PC =12cm. PQ & PR are perpendicular to sides AB &AC respectively. If PQ=15cm and PR=9cm; find the length of PB.

regards,
Nikita

Answer 1

reorder

angle BAC of a triangle ABC is obtuse and AB=AC P is the point in BC such that

In ∆ABC, AC = AB [given]⇒∠B = ∠C [angles opposite to equal sides are equal]In ∆PRC and ∆PQB∠C = ∠B [Proved above]∠PRC = ∠PQB [90° each]⇒∆PRC ~ ∆PQB [AA]⇒PRPQ = RCQB = PCPB [corresponding sides of similar ∆'s are proportional]⇒PRPQ = PCPB⇒915 = 12PB⇒PB = 12 × 159⇒PB = 20 cm