Question

21
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.
the measure of ∠ado is °.
the measure of equal to \\(\frac{1}{2}(\text{m }\overarc{cf} + \text{m }\overarc{de})\\).

Explanation:

Step1: Find $\angle ADO$

A tangent to a circle is perpendicular to the radius at the point of tangency. $OD$ is a radius, $AB$ is tangent at $D$, so $\angle ADO = 90^\circ$.

Step2: Identify the angle formula

The formula $\frac{1}{2}(m\overset{\frown}{CF} + m\overset{\frown}{DE})$ matches the formula for the measure of an angle formed by two intersecting chords: the angle is half the sum of the measures of the intercepted arcs. Here, the intersecting chords are $CD$ and $FE$, forming $\angle CGE$ (or its vertical angle $\angle DGF$).

Answer:

The measure of $\angle ADO$ is $\boldsymbol{90}^\circ$.
The measure of $\boldsymbol{\angle CGE}$ (or $\boldsymbol{\angle DGF}$) is equal to $\frac{1}{2}(m\overset{\frown}{CF} + m\overset{\frown}{DE})$.