Let triangle A B C is right-angled at A . The circle with centre A and radius A B cuts B C and A C internally at D and E respectively. If B D = 20 units and D C = 16 units, then the length A B is equal to

Question

Let triangle A B C is right-angled at A . The circle with centre A and radius A B cuts B C and A C internally at D and E respectively. If B D = 20 units and D C = 16 units, then the length A B is equal to, 6 21 units, 6 10 units, 300 units, 18 units

MARKS App · Accepted Answer

b 2 + r 2 = 36 2 … i Also C D ⋅ C B = C E ⋅ C X 16 ⋅ 36 = b - r b + r ∴ b 2 - r 2 = 16 ⋅ 36 From i and i i 2 b 2 = 36 36 + 16 = 36 ⋅ 52 b 2 = 36 ⋅ 26 ⇒ b = 6 26 units and r = 36 2 - 36 26 = 6 10 units

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