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$If A (5, 2), B (10, 12) and P (x, y) is such that \frac{A P}{P B} = \frac{3}{2}, then the internal bisector of ∠ A P B always passes through$

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(20,32)

(8,8)

(8, -8)

(-8, -8)

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detailed solution

Correct option is B

Let internal bisector of ∠APB meets the side AB at C . We know that ACBC=APPB∴ ACBC=32∴ 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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If A(5,2),B(10,12) and P(x,y) is such that APPB=32 , then the internal bisector of ∠APB always passes through

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$If A (5, 2), B (10, 12) and P (x, y) is such that \frac{A P}{P B} = \frac{3}{2}, then the internal bisector of ∠ A P B always passes through$