Question Video: Finding the Measure of an Arc Using the Relationship Between a Parallel Chord and Tangent | Nagwa Question Video: Finding the Measure of an Arc Using the Relationship Between a Parallel Chord and Tangent | Nagwa

# Question Video: Finding the Measure of an Arc Using the Relationship Between a Parallel Chord and Tangent Mathematics • Third Year of Preparatory School

## Join Nagwa Classes

π is a circle, where line segment π΄π΅ is a chord and line πΆπ· is a tangent. If π΄π΅βπΆπ· and the measure of arc π΄π΅ = 72Β°, find the measure of arc π΅πΆ.

01:33

### Video Transcript

π is a circle, where line segment π΄π΅ is a chord and line πΆπ· is a tangent. If π΄π΅ is parallel to πΆπ· and the measure of arc π΄π΅ is 72 degrees, find the measure of arc π΅πΆ.

Since π΄π΅ is parallel to πΆπ·, where π΄π΅ is a chord and πΆπ· is a tangent, thereβs a theorem we can use. Weβre going to use the theorem that says that the measure of the arcs between a parallel chord and tangent of a circle are equal. So we can say that the measure of arc π΄πΆ must be equal to the measure of arc π΅πΆ. In fact, the question tells us that the measure of arc π΄π΅ is 72 degrees. And we can use the fact that the sum of all the measures of all arcs which make up the circle is 360 degrees. This means that the measure of arc π΄πΆ plus the measure of arc π΄π΅, which is 72 degrees, plus the measure of arc π΅πΆ is 360. Then, we subtract 72 degrees from both sides. And we find that the measure of arc π΄πΆ plus the measure of arc π΅πΆ is 288 degrees.

But earlier, we stated that the measure of arc π΄πΆ is equal to the measure of arc π΅πΆ. So we can say that two times the measure of arc π΅πΆ is 288 degrees. And then we could divide both sides of this equation by two. So the measure of arc π΅πΆ is 288 divided by two, which is in fact 144 degrees. The measure of arc π΅πΆ is 144 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