Three points A,B and C lie on the circle such that AB is the diameter of the circle. Find the angle measure of C.Choices:- 120 deg 270 deg 90 deg 25 deg

1. Break Down the Problem

We have three points $A$, $B$, and $C$ lying on a circle, with $AB$ being the diameter of the circle. We need to find the angle measure at point $C$ formed by the lines $AC$ and $BC$.

2. Relevant Concepts

According to the Inscribed Angle Theorem, an angle subtended by a diameter of a circle is always $90^\circ$. Thus, the angle $\angle ACB$ will be $90^\circ$ because $C$ is on the circle and $AB$ is the diameter.

3. Analysis and Detail

• Point $C$ lies on the circle.
• The line segment $AB$ is the diameter.
• By the Inscribed Angle Theorem, any angle inscribed in a semicircle (formed by the diameter) measures $90^\circ$.

4. Verify and Summarize

Since the theorem consistently applies to inscribed angles in circles, we can conclusively state that the angle at point $C$ is $90^\circ$.

Final Answer

The angle measure at point $C$ is $90^\circ$.