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equal segments from perpendiculars and a diameter

Source: Nordic Mathematical Contest 1995 #1

October 4, 2017

geometryequal segments

Problem Statement

Let

AB

be a diameter of a circle with centre

O

. We choose a point

Q

on the circumference of the circle such that

R

and

AB

are perpendicular to each other. Let

P

be an arbitrary point on the (smaller) arc

AB

and let the lines

CP

and

AB

meet at

Q

. We choose

R

on

AP

so that

RQ

and

AB

are perpendicular to each other. Show that

BQ =QR

.

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