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Question

If d1,d2,d3 are the diameters of the three ascribed circles of a triangle, then d1d2+d2d3+d3d1 is equal to


A

4s2

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B

2

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C

42

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D

22

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Solution

The correct option is A

4s2


Explanation for the correct option:

Step 1. Find the value of d1d2+d2d3+d3d1:

As we know, d1=2r1,d2=2r2,d3=2r3

Also we have, r1=(sa)

r2=(sb)

r3=(sc)

Step 2. Put the values of r1,r2,r3 in given expression, we get

d1d2+d2d3+d3d1=4(r1r2+r2r3+r3r1)=421(sa)(sb)+1(sb)(sc)+1(sc)(sa)=42sc+sa+sb(sa)(sb)(sc)=423s(a+b+c)(sa)(sb)(sc)=423s2s(sa)(sb)(sc)=42s(sa)(sb)(sc)=42s2s(sa)(sb)(sc)=42s22=4s2

Hence, Option ‘A’ is Correct.


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