Question

In a right angled triangle, the length of the sides are $a$ and $b (0< a < b )$. A circle passes through the mid-point of the smaller side and touches the hypotenuse at its mid-point.

• A. centre of the circle is $\left(\frac{2 a^2-b^2}{4 a}, \frac{b}{4}\right)$
• B. centre of the circle is $\left(\frac{2 b ^2- a ^2}{4 b }, \frac{ b }{4}\right)$
• C. radius of the circle is $\frac{b \sqrt{a^2+b^2}}{4 a}$
• D. radius of the circle is $\frac{a \sqrt{a^2+b^2}}{4 b}$

Answer 1

Answer: (A), (C)

Correct answer is (a) centre of the circle is $\left(\frac{2 a^2-b^2}{4 a}, \frac{b}{4}\right)$Correct answer is (c) radius of the circle is $\frac{b \sqrt{a^2+b^2}}{4 a}$