Russia’s Prime Minister sets sixth formers a geometry puzzle

[SydneyRover]

From the Guardian:

This was a challenge Russia’s Prime Minister, Mikhail Mishustin, gave to a class of Russian sixth formers earlier this month.

Some of our younger members that have retained a bit of geometry may be able to solve this without looking at the answer below. I had to remind myself of what a few terms meant but still failed.

''Given a circle with a diameter marked on it, and any point (except where the diameter meets the circumference) on the circle, can you find a way to draw a line from the point that hits the diameter at a right angle.

What makes this question interesting is the banning of measuring devices. Compass and marked ruler are verboten. All you are allowed is an unmarked ruler to draw straight lines.

Given information:

1) The angle subtended by a point on a circle to the two ends of a diameter is a right angle.

2) The altitude of a triangle is the line from a corner that meets the opposing side at a right angle. In acute triangles the three altitudes will always intersect''

https://www.theguardian.com/science/2021/sep/20/did-you-solve-it-russias-prime-minister-sets-a-geometry-puzzle