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Question

A triangle ABC is drawn to circumscribe a circle such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 20 cm respectively. If the area of the triangle is 120 cm2, what is the value of AB + AC?


A

48 cm

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B

36 cm

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C

24 cm

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D

60 cm

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Solution

The correct option is B

36 cm


Let P,Q,R be the points where sides AB,BC and AC meet the circle respectively.

The tangents drawn from an external point to the circle are equal in length.

So, BP = BQ = 4 cm

Also, CR = CQ = 20 cm

Let AP = AR = x cm

Then,

AB = 4+x

AC = 20+x

BC = 24

Area of the traingle
=s(sa)(sb)(sc)

Here ,
s=a+b+c2 = (4+x)+(20+x)+242=24+x

Area =
x(24+x)(20)(4)=120

Squaring on both sides, we get,

x2+24x180=0

(x6)(x+30)=0

x=6
(As x = - 30 cannot be length od a side)

So, the sides are

BC = 24 cm

AB = 4+x = 10 cm

AC = 20+x = 26 cm

Therefore , AB + AC = 36 cm


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