# The vertex of angle BAC lies inside of a circle. Prove that the value of angle BAC is equal to half the sum of angle measures of the arcs of the circle confined inside angle itself and inside the angle symmetric to it through vertex A.

Marilyn Cameron 2022-10-24 Answered
The vertex of angle $\mathrm{\angle }BAC$ lies inside of a circle. Prove that the value of angle $\mathrm{\angle }BAC$ is equal to half the sum of angle measures of the arcs of the circle confined inside angle itself and inside the angle symmetric to it through vertex $A$.
So I don't understand how to prove this. I've already drawn a diagram but I can't figure out how to prove this. Please help! Thank you!
You can still ask an expert for help

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it

## Answers (1)

Jean Deleon
Answered 2022-10-25 Author has 14 answers
Let $BD$ and $CE$ be chords of the circle and $BD\cap CE=\left\{A\right\}$.
Thus,
$\measuredangle BAC=\measuredangle BEA+\measuredangle EBA=\frac{1}{2}\stackrel{^}{BC}+\frac{1}{2}\stackrel{^}{DE}.$
###### Did you like this example?

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it