Question

Incentre of the triangle whose vertices are (6, 0)(0, 6)and(7, 7) is-

• A. $\left( \frac{9}{2},\frac{9}{2} \right)$
• B. $\left( \frac{7}{2},\frac{7}{2} \right)$
• C. $\left( \frac{11}{2},\frac{11}{2} \right)$
• D. None of these

Answer 1

Answer: (A)

$\left( \frac{9}{2},\frac{9}{2} \right)$

Answer 2

A (6, 0) ; B(0, 6) ; C (7, 7)

$\mathrm { AB } = \sqrt { 72 } = 6 \sqrt { 2 }$ $\mathrm { BC } = \sqrt { 50 } = 5 \sqrt { 2 }$ $\mathrm { CA } = \sqrt { 50 } = 5 \sqrt { 2 }$

\ in centre

ŗ $\left( \frac{6 \times 5\sqrt{2} + 0 \times 5\sqrt{2} + 7 \times 6\sqrt{2}}{6\sqrt{2} + 5\sqrt{2} + 5\sqrt{2}},\frac{0 \times 5\sqrt{2} + 6 \times 5\sqrt{2} + 7 \times 6\sqrt{2}}{6\sqrt{2} + 5\sqrt{2} + 5\sqrt{2}} \right)$

ŗ $\left( \frac{72\sqrt{2}}{16\sqrt{2}},\frac{72\sqrt{2}}{16\sqrt{2}} \right)$ ŗ $\left( \frac{9}{2},\frac{9}{2} \right)$