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Triangle ABC is right angled at A. The c...

Triangle ABC is right angled at A. The circle with centre A and radius AB cuts BC and AC internally at D and E respectively. If BD=20 and DC=16 then the length AC equals

A

`6sqrt(21)`

B

`6sqrt(26)`

C

30

D

32

Text Solution

Verified by Experts

The correct Answer is:
B
`b^(2) +r^(2) = (36)^(2)` (1)
Also, `CD. CB = CE. CX`
`:. 16. 36 = (b-r) (b+r)`
`:. b^(2) -r^(2) = 16 xx 36` (2)
From (1) and (2)
`2b^(2) + 36 (36+16) = 36 xx 52`
`rArr b = 6 sqrt(26)`
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