Qm
Brainteasers

The angle in a semicircle

geometrycirclesthalesproof

A circle has a diameter AB. Let C be any other point on the circle.

Prove that the angle ACB is a right angle, whatever the position of C. Then use it to answer: a carpenter wants to check that a corner of a board is exactly square using only a circular plate; how?

Show a hint

Draw the radius from the centre O to C. That creates two isosceles triangles, OAC and OBC.

Your answer

Solving needs a free account

Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.

Create a free accountSign in

Discussion

Sign in to join the discussion · reading is open to everyone

💡 Discussion rules

  1. No full solutions here. Hints and approaches only.
  2. Complexity, edge cases and intuition are the point.
  3. Interview experiences are welcome. Respect your NDAs.

Loading discussion…

Learn the concepts

The theory behind this question.

The Rope Around the EarthChoosing Coordinates That Kill the ProblemGeometric Probability PuzzlesProof Techniques: Direct, Contrapositive, ContradictionReuleaux Shapes and Why Manhole Covers Are Round

Related questions

Why a football always has exactly twelve pentagonsThe midpoint of a sliding ladderThe angles at the points of a starThe angle between two face diagonals of a cubeThe angles of a twenty-sided polygon
All questions →