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) 6sqrt21 (B) 6sqrt26 (C) 30 (D)32

Options

A. `6sqrt(21)`
B. `6sqrt(26)`
C. 30
D. 32

Answer

B

Explanation

`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)`