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In a triangle A B C , right angled at A ...

In a triangle `A B C ,` right angled at `A ,` on the leg `A C` as diameter, a semicircle is described. If a chord joins `A` with the point of intersection `D` of the hypotenuse and the semicircle, then the length of `A C` is equal to `(A BdotA D)/(sqrt(A B^2+A D^2))` (b) `(A BdotA D)/(A B+A D)` `sqrt(A BdotA D)` (d) `(A BdotA D)/(sqrt(A B^2-A D^2))`

A

`(AB*AB)/(sqrt(AB^(2)+AB^(2)))`

B

`(AB*AD)/(AB+AD)`

C

`sqrt(AB*AD)`

D

`(AB*AD)/(sqrt(AB^(2)-AD^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
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