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Here AP and OB are parallel to each other
So Angle OBC = Angle APB (corresponding angles)
Angle PAB = Angle OBA ( alternate interior angle)
And Angle ABO = Angle OBC ( bisected angles)
Hence PB = PA (isosceles triangle property) (1)
And similarly from other parallel lines we will get :
CQ = AC (2)
And Perimeter of the triangle is AB + BC + AC
Or AB + BC + AC = CQ + BC + PB = PQ using (1) and(2)
( Hence proved)
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