Tangent Radius Angle

Key idea

A tangent and the radius drawn to the point of contact form a right angle. So the angle between the tangent and the radius is 90°.

How to solve

1. Identify the point of contact between the line and the circle.
2. Locate the radius that goes from the center of the circle to that point.
3. Use the tangent-radius fact: the radius is perpendicular to the tangent at the point of contact.
4. Fill in the missing angle as 90° whenever the angle is exactly between the tangent and that radius.

What to watch for

• Make sure the given angle really uses the tangent and the radius at the contact point.
• If another angle is involved, use the right angle relationship first, then combine it with any other angle facts.

Check your answer

Your result should match the perpendicular relationship: tangent ⟂ radius, so the angle is 90°. If the exercise asks for a simplified final answer, 90° is already in simplest form.