Find the measure of angle 𝐶.
In this question, we are asked to find the measure of angle 𝐶 inside the triangle. We will do this by recalling some of the key properties of circles. The two chords 𝐴𝐵 and 𝐴𝐶 are equidistant from the center of the circle point 𝑀. We know this since line segment 𝑀𝐸 is equal to line segment 𝑀𝐷.
One of our circle theorems states that if two chords are equidistant from the center of a circle, their lengths are equal. This means that the chords 𝐴𝐵 and 𝐴𝐶, which are two sides of our triangle, are equal in length. This means that triangle 𝐴𝐵𝐶 is isosceles. In an isosceles triangle, two angles are equal. In this case, the measure of angle 𝐴𝐵𝐶 is equal to the measure of angle 𝐴𝐶𝐵. This can also be written as the measure of angle 𝐵 is equal to the measure of angle 𝐶. Since we are told that angle 𝐵 is 70 degrees, the measure of angle 𝐶 is also equal to 70 degrees.