Question

1. In circle o, chord AB and tangent CAD are drawn. It is known that mAB=116 . Find each of the

Answer 1

Given:

m(ar AB) = 116°

To find:

1. The measure of arc BEA.

2. The measure of ∠CAB

3. The measure of ∠BAD

Solution:

1. The measure of arc of full circle is 360°.

m(ar AB) + m(ar BEA) = 360°

116° + m(ar BEA) = 360°

Subtract 116° from both sides.

m(ar BEA) = 244°

2. Using the tangent-chord angle theorem:

$\Rightarrow m\angle CAB = \frac{1}{2} m(ar \ AB)$

$\Rightarrow m\angle CAB = \frac{1}{2} \times 116^\circ$

⇒ m∠CAB = 58°

3. Using the tangent-chord angle theorem:

$\Rightarrow m\angle BAD = \frac{1}{2} m(ar \ BEA)$

$\Rightarrow m\angle BAD = \frac{1}{2} \times 244^\circ$

⇒ m∠BAD = 122°

Using the fact that it is supplementary to ∠CAB.

⇒ m∠CAB + m∠BAD = 180°

⇒ 58° + m∠BAD = 180°

Subtract 58° from both sides.

⇒ m∠BAD = 122°