Question

In the given figure AB = 8 cm. M is the midpoint of AB.

Semi circles are drawn on AB, AM and MB as diameter. A circle with centre ‘O’ touches all three semi circles as shown. Prove that the radius of this circle is .

Answer 1

From the figure, it can be observed that ΔOMD is a right-angled triangle.

It is given that AB = 8 cm

∴ PM = MB = AM = = 4 cm

Here, OM = PM – PO = 4 – x, MD = = 2 cm and OD = x + 2

Applying Pythagoras theorem in right ΔOMD, we have:

Hence, the radius of the circle is.