Question

ad is tangent to circle b at point c. what is the measure of ∠bca? 180° 90° 50° 40°

Explanation:

Step1: Recall the property of tangent to a circle

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \(BC\perp AD\) (since \(AD\) is tangent to circle \(B\) at \(C\)).

Step2: Use the definition of perpendicular lines

If two lines are perpendicular, the angle between them is \(90^{\circ}\). In \(\triangle BCA\), \(\angle BCA\) is the angle between radius \(BC\) and tangent \(AD\).

Answer:

\(90^{\circ}\)