Thread: Thales Theorem

Prove the following.

If the vertices of triangle ABC lie on a circle and AB is a diameter of that circle, then angle ACB is a right angle.

I think that I need to use the Isosceles Triangle Theorem and the Angle Sum of a Triangle Theorem

Originally Posted by MATNTRNG

Prove the following.

If the vertices of triangle ABC lie on a circle and AB is a diameter of that circle, then angle ACB is a right angle.

I think that I need to use the Isosceles Triangle Theorem and the Angle Sum of a Triangle Theorem

See diagram

Thales theorem is a special case of the inscribed angle theorem which states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle. Therefore, the angle does not change as its apex is moved to different positions on the circle.

If angle inscribed in a circle and the central angle both subtend the semicircle then the central angle equals 180° and the angle inscribed equals half the central angle or 90°.