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Let ABC be a triangle with /A=45^0dot Le...

Let ABC be a triangle with `/_A=45^0dot` Let P be a point on side BC with PB=3 and PC=5. If O is circumcenter of triangle ABC, then length OP is `sqrt(18)` (b) `sqrt(17)` (c) `sqrt(19)` (d) `sqrt(15)`

A

`sqrt(18)`

B

`sqrt(17)`

C

`sqrt(19)`

D

`sqrt(15)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let OP = x
Circumradius = R
`:. (BC)/(sin 45^(@)) = 2R`
or `R = 4sqrt2`
Now `PB.PC = PM.PN`
or `15 = (R -x) (R + x)`
or `x = sqrt17`
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