# In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region

**Solution:**

We use the concepts of areas of circles and areas of triangles to solve the problem.

AB and CD are diameters of the circle with center O

∴ OD = OC = OA = OB = R = 7 cm (radius of the circle)

∴ AB = 2R = 14 cm

Radius of shaded circular region, r = OD/2 = 7/2 cm

Area of the shaded smaller circular region = πr²

= π (7/2 cm)^{2}

= 22/7 × 7/2 × 7/2 cm^{2}

= 77/2 cm^{2}

= 38.5 cm^{2}

Area of the shaded segment of larger circular region = Area of semicircle ACB - Area of ΔABC

= 1/2 π(OA)^{2} - 1/2 × AB × OC

= 1/2 πR^{2} - 1/2 × 2R × R

= 1/2 × 22/7 × (7 cm)^{2} - 1/2 × 14 cm × 7cm

= 77 cm^{2} - 49 cm^{2}

= 28 cm^{2}

Area of shaded region = Area of the shaded smaller circular region + Area of the shaded segment of larger circular region

= 38.5 cm^{2} + 28 cm^{2}

= 66.5 cm^{2}

**Video Solution:**

## In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.3 Question 9:

In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region

The area of the shaded region if AB and CD are two diameters of a circle with center O perpendicular to each other and OD is the diameter of the smaller circle is 66.5 cm^{2}