Question

Select the correct answer from each drop-down menu.The center of the circle is at O. Segment AB is tangent to circle O at point D.DBOFThe measure of XADO isThe measure ofVequal to (mCF +mDE)ResetNext

Answer 1

Solution

Step

A line from the center of a circle to the tangent is perpendicular to the line of the tangent.

The measure of angle

Step 2

Angles of Intersecting Chords Theorem

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

$\begin{gathered} m∠CGF\text{ = }\frac{1}{2}(mCF\text{ + mDE\rparen} \\ \\ m\angle DGE\text{ = }\frac{1}{2}(mCF\text{ + mDE\rparen } \end{gathered}$