A circle is inscribed in the triangle ABC whose sides are given as AB = 10, BC = 8, CA = 12 units as shown in the figure. The value of AD × BF is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 21 units.
| Understanding | Application |
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The length of the tangent drawn from the same external point on a circle is same. Let AD=AE=x, CD=CF=y and BE=BF= z |
AB = AE+EB 10 = x + z ... (i) BC = BF + FC 8 = z + y ....(ii) AC = AD + DC 12 = x + y ... (iii) Adding equation i, ii and iii, we get 30 = x + z + z + y + x + y 30 = 2(x + y + z) x + y + z = 15 From equation ii, z + y = 8 x = 15 - 8 =7 From equation (iii) x + y = 12 z = 15 - 12 = 3 We need to find value of (AD)(BF) = (x)(z) = (7)(3) = 21 |