Q) In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then :
(i) find the length of the chord AB.
(ii) find the area of shaded region.
(Take π = 3.14 and √3 = 1.73) π

Ans: 

Let’s start with Δ AOB,

∠ AOB = 60⁰

OA = OB (radii of same circle)

∴ ∠ OAB = ∠ OBA (angles opposites to equal sides)

∵ ∠ AOB = 60⁰ , ∴ ∠ OAB = ∠ OBA = 60⁰  (angles of same triangle)

∴ Δ AOB is an equilateral triangle

∴ AB = OA = 10 cm

Therefore length of chord AB is 10 cm

(ii) Area of shaded region = Area of semicircle – area of equilateral triangle OAB

=

=

= (1.57 – 0.4325) x 100

= 1.1425 x 100 = 114.25 cm²

Therefore, the area of shaded region is 114.25 cm²

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