Question

Chord AC and DE intersect at T $\overline{AB}$ is tangent to the circle at A mAD = 114, mEC = ${36}^{\circ }$ and AE = 75
a. Find $\angle CAB$
b. Find $\angle ATD$

Answer 1

a. By theorem 1
$m\angle CAB$ = $\frac{1}{2}$ mAC
= $\frac{1}{2}$ (mSR + mRT)
= $\frac{1}{2}$ $({75}^{\circ }+{36}^{\circ })$
$=\frac{1}{2}\left(111\right)$
= 55.5
b. By theorem 2
$m\angle ATD=\frac{1}{2}$ (mEC + mAD)
= $\frac{1}{2}({36}^{\circ }+{114}^{\circ })$
=$\frac{1}{2}$(150)
= 75