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Find πβ πΆ.

Find the measure of angle πΆ.

In this question, we are asked to find the measure of angle πΆ inside the triangle. We will do this by recalling some of the key properties of circles. The two chords π΄π΅ and π΄πΆ are equidistant from the center of the circle point π. We know this since line segment ππΈ is equal to line segment ππ·.

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 π΄π΅ and π΄πΆ, which are two sides of our triangle, are equal in length. This means that triangle π΄π΅πΆ is isosceles. In an isosceles triangle, two angles are equal. In this case, the measure of angle π΄π΅πΆ is equal to the measure of angle π΄πΆπ΅. This can also be written as the measure of angle π΅ is equal to the measure of angle πΆ. Since we are told that angle π΅ is 70 degrees, the measure of angle πΆ is also equal to 70 degrees.

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