Question

Tangent AD and secant FB intersect at point C, the point of tangency. what is the measure of DCF?

Answer 1

∠DCF is 100°

Explanation:

Given tangent AD and secant FB intersect at point C, the point of tangency. We have to find the measure of ∠DCF.

As, ∠COF=160°

In ΔCOF, by Angle Sum Property of triangle

∠OCF+∠COF+∠OFC=180°

⇒ ∠OCF+160°+∠OCF=180° (∵OC=OF)

⇒ 2∠OCF=20° ⇒ ∠OCF=10°

Now, we have to find the ∠DCF

∠DCF=∠DCO+OCF

As radius from the center of circle to the point of tangency is perpendicular to the tangent line.

∠DCF=∠DCO+OCF

=90°+10°=100°