Question

Circle O is shown. Secants C A and C E intersect at point C outside of the circle to form an angle with measure 36 degrees. Secant C A intersects the circle at point B, and secant C E intersects the circle at point D. Arc B D is 48 degrees. In circle O, what is mArc A E?

Answer 1

its C, 120

Explanation:

got it right on the test

Answer 2

120°

Explanation:

The external angle <C outside the circle can be expressed in terms of length of arc AE and BD using the formula below.

<C =
`(AE-BD)/(2) \\`

Next is to make the length of arc AE the subject of the formula;

<C =
`(AE-BD)/(2) \\`

cross multiply

`2<C = AE-BD`

add BD to both sides of the equation

`2<C+BD = AE-BD+BD\\2<C +BD = AE`

`AE = 2<C +BD`

Given

<C = 36°

arc BD = 48°

Substitute the given parameters into the formula;

`AE = 2<C +BD\\AE = 2(36)+48\\AE = 72+48\\AE = 120^0\\`

Hence mArc is 120°