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  • Let r be the radius of incircle of triangle formed by joining centres of <img alt="\mathrm{(x-a)^2+(y-b)^2=9,(x-a)^2+(y-b-7)^2=16}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmath

Let r be the radius of incircle of triangle formed by joining centres of \mathrm{(x-a)^2+(y-b)^2=9,(x-a)^2+(y-b-7)^2=16} and circle touching above two circles and having radius 5 units.The value of \mathrm{r^{2}} is ________

Option: 1

3


Option: 2

5


Option: 3

8


Option: 4

9


Answers (1)

best_answer

All three circles touch each other externally,

\mathrm{\begin{aligned} & \therefore \quad C_1 C_2=7 \\ & C_2 C_3=9 \text { and } C_3 C_1=8 \\ & \text { Also, } s=\frac{7+8+9}{2}=12 \end{aligned}}

\mathrm{\Delta=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{12 \times 5 \times 3 \times 4}=12 \sqrt{5}}

\mathrm{r=\frac{\Delta}{s}=\frac{12 \sqrt{5}}{12}=\sqrt{5} \Rightarrow r^2=5}

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