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

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.

What is the Tangent Theorem?

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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