TS EAMCET · Maths · Properties of Triangles

Let $A$ be the area of in-circle and $A_{1}, A_{2}, A_{3}$ be the areas of ex-circles of a triangle. If $A_{1} = 4, A_{2} = 9, A_{3} = 16$ , then $A =$

A $81$
B $\frac{61}{169}$
C $\frac{144}{61}$
D $\frac{144}{169}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{144}{169}$

Step-by-step Solution

Detailed explanation

Given, The areas of ex-circles of a triangle, A1=4, A2=9 & A3=16 Now finding radius by formula we get, A1=4⇒πr12=4 ..........1 A2=9⇒πr22=9 ............2 A3=16⇒πr32=16 ...........3 Now we know that relation…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let A be the area of in-circle and A1,A2,A3 be the areas of ex-circles of a triangle. If A1=4,A2=9,A3=16, then A=

Step-by-step Solution

Let $A$ be the area of in-circle and $A_{1}, A_{2}, A_{3}$ be the areas of ex-circles of a triangle. If $A_{1} = 4, A_{2} = 9, A_{3} = 16$ , then $A =$