KVPY SA Exam 2011 Question Paper

Question : 6 of 80

Marks: +1, -0

Let ABC be a triangle with ∠B = 90°. Let AD be the bisector of ∠A with D on BC. Suppose AC = 6 cm and the area of the triangle ADC is

10 \cm^2

. Then the length of BD in cm is equal to

Solution:

From angle bisector theorem

r/6=p/q

qr=6p

...(1)
Area of ∆ADC

= 10 \cm^2

1/2(\DC)(\AB)=10

⇒1/2qr=10⇒qr=20

From (1)

⇒ 20 = 6 p

p=20/6=10/3

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