In the figure above segment AB is tangent to circle C and ha

In the figure above, segment AB is tangent to circle C and has a length of 12. If circle C has a radius of 4, what is the area of Delta ABC? (A) 12 (B) 18 (C) 24 (D) 30 (E) 36

Solution

By the theorem of tangents the radius to the tangent is at 90o. Therefore the radius is the height of traingle ABC from C to the base AB.

Therefore Base (AB) = 12 and Height= Radius = 4.

Therefore Area = (1/2) x Base x Height = (1/2) x 12 x 4 = 24 (OPTION C)