Line $ef$ is tangent to circle $g$ at point $a$. If the measure of angle $eag$ is $95°$, what is the measure of the angle between the tangent and the radius at point $a$?

• A. $180°$
• B. $95°$
• C. $85°$
• D. $90°$

Answer: (D)

Verified step by step guidance

1. Recall the fundamental property of a tangent line to a circle: the tangent line at a point on the circle is perpendicular to the radius drawn to that point.
2. This means the angle between the tangent line and the radius at the point of tangency is always 90 degrees.
3. Given that line ef is tangent to circle g at point a, the radius ga meets the tangent ef at point a.
4. Therefore, the angle between the tangent line ef and the radius ga at point a is a right angle, which measures 90 degrees.
5. The given angle e a g measuring 95 degrees is an external angle and does not affect the perpendicularity between the tangent and radius at point a.