In a given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the

In a given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

📘 K C Sinha Class 10 Maths | Area of Shaded Region in Circle | Mensuration

In this video, we solve an important mensuration problem involving a circle, chords, and sectors from K C Sinha Class 10 Mathematics.

Question:
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

This question uses concepts of:
✔ Area of a circle
✔ Area of a sector
✔ Area of a triangle inscribed in a circle
✔ Diameter theorem
✔ Shaded region problems

Since CB passes through the centre O, CB is the diameter.

Using Pythagoras' theorem:
24² + 7² = 625 = 25²

Therefore,
CB = 25 cm = Diameter

Radius = 12.5 cm

A=πr^2

The shaded region consists of:

Area of the semicircle above CB minus area of △ABC
Area of sector BOD (90°)

Total shaded area

= (1/2 × π × 12.5² − 1/2 × 24 × 7)

(90/360 × π × 12.5²)

= (245.54 − 84) + 122.77

= 284.31 cm² (approximately)

🔹 K C Sinha Class 10 Maths Solutions
🔹 Circle and Sector Problems
🔹 Shaded Region Questions
🔹 Board Exam Preparation
🔹 Step-by-Step Explanation

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