## Problem

PQR is a right triangle. It is free to move so that P is always on the x-axis and R is on the y-axis. Show that the point Q (right angle) always lies on a straight line passing through the origin.

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Form is valid through April 2019

## Solution

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The first one to send a correct solution was Eli.

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Here is my solution:

As the length of PR is fixed and angles Q and O are right angles, OPR is a cyclic quadrilateral.So angles ROQ and RPQ are equal (subtended by the same arc.

But the second angle is a constant.Thus angle ROQ is also a constant and point Q lies on a straight line passing through the origin. Proved.

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