A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of triangle in square inches is.
Explanation:
Here, BM = BN = 4 (Radius of the circle)
BC = 10 cm, hence, MC = CO = 10 – 4 = 6 cm.
Let AN = x, hence, AO = x
In right ∆ABC, AB2 + BC2 = AC2
⇒ (x + 4)2 + 102 = (x + 6)2
⇒ x2 + 16 + 8x + 100 = x2+ 12x + 36
⇒ 4x = 80
⇒ x = 20
∴ Area of triangle ABC = ½ × AB × BC = ½ × (20 + 4) × 10 = 120 sq. inches.
Hence, 120.
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