Based on the tangent theorem, m∡ADO = 90°.
Based on the angles of intersecting chords theorem, m∡CGF = 1/2(mCF + mDE).
What is the Angles of Intersecting Chords Theorem?
The angles of intersecting chords theorem states that when two chords in a circle intersect, the angle formed inside the circle at the point of intersection has a measure that is half of the sum of the measures of the intercepted arcs that are formed by the angle and its vertical angle.
<h3>What is the Tangent Theorem?</h3>
According to the tangent theorem, if a line is tangent to a circle, the segment forms a right angle at the point of tangency with the radius of the circle.
Since line AB is tangent to circle O at point D, therefore, based on the tangent theorem:
The measures of angle ADO = 90°
Chord CE and DF intersect in the circle, therefore, based on the angles of intersecting chords theorem:
The measure of CGF = 1/2(mCF + mDE).
Learn more about the tangent theorem on:
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