Segment AB measures 4 cm and is a diameter of circle P. In triangle ABC, point C is on circle P and BC = \(1\) cm. What is the area of the shaded region?
+128406 ABC forms a right triangle with a leg of 1 and a hypotenuse of 4
The other leg = sqrt (4^2 - 1^2 ) = sqrt (15)
The area of this triangle = product of the leg lengths / 2 = (1/2)(1) (sqrt 15) = sqrt 15 / 2
Area of the circle = pi (AP)^2 = pi * 2^2 = 4pi
So.....the shaded region is [ 4pi - sqrt (15) / 2 ] cm^2 ≈ 10.63 cm ^2
