Question

in an isosceles triangle ABC AB =AC and P is any point on produced sides BC, PQ and PR are perpendicular on sides AB and AC from the point P respectively BAC is perpendicular on side AC from point P prove that PQ - PR=BS​

Answer 1

hey there !

Answer:

Given.

AB= AC;

PQ and PR are perpendicular on sides AB and AC from the point P respectively. BS is perpendicular on side AC from point B

Formula used.

Area of triangle =  × Base × Height

As triangle ABC and triangle ACP combines to form triangle ABP

Area of triangle ABP = Area of triangle ABC + Area of triangle ACP

Area of triangle ABP =  × Base × Height

× AB × PQ

Area of triangle ABC =  × Base × Height

× AC × BS

Area of triangle ACP =  × Base × Height

× AC × PR

⇒  × AB × PQ =  × AC × BS +  × AC × PR

As AB = AC (Given)

⇒  × AC × PQ =  × AC × BS +  × AC × PR

Taking common ×AC get removed

⇒ PQ = BS + PR

∴ PQ – PR = BS

Hence proved

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