Question Video: Finding the Measure of an Angle in the Triangle of a Circumcircle | Nagwa Question Video: Finding the Measure of an Angle in the Triangle of a Circumcircle | Nagwa

# Question Video: Finding the Measure of an Angle in the Triangle of a Circumcircle Mathematics • Third Year of Preparatory School

## Join Nagwa Classes

Find πβ πΆ.

01:26

### Video Transcript

Find the measure of angle πΆ.

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

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

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions