Question

Find each value and measure. Assume that segments that appear to be tangent are tangent.

Answer 1

Given:

Given that AC and BD are chords of the circle.

The two chords intersect at the point E which makes an angle 93°

The measure of arc BC is 161°

We need to determine the measure of arc AD.

Measure of arc AD:

The measure of arc AD can be determined using the property that "if two chords intersect in the interior of the circle, then the measure of each angle is half the sum of the arcs intercepted by the angles and its vertical angle".

Thus, applying the above theorem, we have;

$m \angle E=\frac{1}{2}(m \widehat{BC}+m \widehat{AD})$

Substituting the values, we have;

 $93^{\circ}=\frac{1}{2}(161^{\circ}+m \widehat{AD})$

$186^{\circ}=161^{\circ}+m \widehat{AD}$

 $25^{\circ}=m \widehat{AD}$

Thus, the measure of arc AD is 25°