# Math Help - proportion similarity

1. ## proportion similarity

I have a question, haven't been able to solve them..

PQ and PR are tangents to a circle with centre O,and A is any point on QR..PB is the perpendicular from P to OA produced and meets it at B..prove that the points O,Q,B,P,R,are concyclic..if QR or RQ produced meets PB produced at C,prove that qr is divided harmonically at A and C..

2. For the first part:
In quadrilateral $PROQ$, $m(\widehat{PRO})=m(\widehat{PQO})=90^{\circ}\Right arrow PROQ$ is inscribable.
In quadrilateral $POQB$, $m(\widehat{PQO})=m(\widehat{PBO})=90^{\circ}\Right arrow POQB$ is inscribable.
The two quadrilaterals have in common the points $P,O,Q$, so all the five points are cyclic.