AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD.
Explanation:
Since AB is the diameter of the circle, ∠ACB would be right angle. In this triangle, we know AB = 15 and AC = 12. So we can find BC. Hence, BC = 9. Since BC = BD, AD = AC (similar triangles). Hence, area of ΔACB = Area of Δ ABD =12 × AC × CB = 12 × 12 × 9 = 54 cm2
So the area of quadrilateral ACBD = 2 × 54 = 108 sq. cm.
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