Answer:
∠DCF is 100°
Step-by-step 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°
