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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 - CBSE Class 10 - Mathematics

ConceptProblems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle

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.

Solution

BC is the diameter of the circle passing through the centre O.

Now,

∆ABC is a right angles triangle, right angled at A.      (Angle subtended by the diameter on the circumference of the circle is 90°)

In right ∆ABC,

BC2 = AB2 + AC2

= (7)2 + (24)2

= 49 + 576

= 625

∴ BC = 25 cm

Also,

∠COD + ∠BOD = 180° (Linear pair angles)

⇒∠COD = 180° − 90° = 90°

Now,
Area of the shaded region = Area of sector OCABDO − Area of ∆ABC

= 270^@/360^@ xx pi((BC)/2)^2 - 1/2 xx AB xx AC  (∵ 360° - 90° = 270° )

= 3/4 xx 3.14 xx (25/2)^2 - 1/2 xx 7 xx 24

= 367.97 - 84

= 283.97 cm2 (Approx)

Hence the area of shaded region is approximately 283.97 cm2

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Solution 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 Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle.
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