Question Video: Finding the Sum of Two Inscribed Arcs between Two Intersecting Chords given the Angle between the Chords | Nagwa Question Video: Finding the Sum of Two Inscribed Arcs between Two Intersecting Chords given the Angle between the Chords | Nagwa

# Question Video: Finding the Sum of Two Inscribed Arcs between Two Intersecting Chords given the Angle between the Chords Mathematics • Third Year of Preparatory School

## Join Nagwa Classes

In the given figure, find π the arc π΄πΆ + π the arc π΅π·.

01:47

### Video Transcript

In the given figure, find the measure of the arc π΄πΆ plus the measure of the arc π΅π·.

Letβs look carefully at the diagram weβve been given. We have two chords, π΄π΅ and πΆπ·, which intersect inside a circle. Weβre given the measure of one of the angles formed at the point of intersection and asked to find the sum of the measures of the arcs π΄πΆ and π΅π·, which are the arcs now highlighted in orange and pink on our diagram.

To answer this question, we need to recall a theorem about the measures of angles formed by two chords that intersect inside a circle. This tells us that the measure of an angle between two chords is one-half the sum of the measures of its intercepted arc and its opposite arc. In this figure, the arc intercepted by the angle of 112 degrees is the arc π΅π·. And its opposite arc or the arc intercepted by its opposite angle is the arc π΄πΆ.

We can therefore form an equation. 112 degrees is equal to one-half the measure of the arc π΄πΆ plus the measure of the arc π΅π·. And thatβs great, because it is the measure of the arc π΄πΆ plus the measure of the arc π΅π· that weβre looking to find. We can work this out by multiplying both sides of the equation by two. This gives 224 degrees is equal to the measure of the arc π΄πΆ plus the measure of the arc π΅π·.

So by recalling the angles of intersecting chords theorem, we found that the measure of the arc π΄πΆ plus the measure of the arc π΅π· is 224 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