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If A(5,2),B(10,12) and P(x,y) is such th...

If `A(5,2),B(10,12)` and `P(x,y)` is such that `(AP)/(PB) = (3)/(2)`, then then internal bisector of `/_APB` always passes through (a) ( 20,32) (b) (8,8) (c) (8,-8) (d) (-8,-8)

A

`(20,32)`

B

`(8,8)`

C

`(8,-8)`

D

`(-8,-8)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let internal bisector of `/_APB` meets the side AB at C. We know that `(AC)/(BC) =(AP)/(PB)`
`:. (AC)/(BC) =(3)/(2)`
`:.` coordinates of C are `((3(10)+2(5))/(3+2),(3(12)+2(2))/(3+2))` or (8,8) Hence the internal bisector of `/_APB` always passes through point (8,8)
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