Question

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Answer 1

Hello again friend

As ∠ ABD = ∠ XYD = ∠ CDB = 90°

⇒ AB || XY || CD

In Δ ABD

AS AB || XY

So,

DY/BD = c/a

⇒ DY = c/a(BD) ....(1)

In Δ BDC

AS CD || XY

So,

BY/BD = c/b

BY = c/b(BD) ......(2)

Adding (1) and (2), we get

DY + BY = c/a(BD) + c/b(BD)

BD = c(1/a + 1/b)BD

1/c = 1/a + 1/b

1/c = (a+b)/ab

c(a+b) = ab

Hence proved.

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