Question

In a circle of radius 12 cm, arc PQ subtends the angle of 30° at the centre. Find area between the arc PQ and chord PQ

Answer 1

Above the explanation of the answer is properly done with all steps.....
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Answer 2

Area between the arc PQ and chord PQ is 12 ( π-3)sq cm

Radius of the circle = r = 12cm  ( Given )

Angle subteneded at the centre = Ф = 30° = 30 × π/180

= π/6

Area of sector = 1/2 r²Ф

= 1/2 × 12² × π/6

= 12π sq cm

In ΔOOR, sin 30° = QR/OQ

Therefore, OR = OQ sin 30° = 12 × 1/2 = 6

Area of ΔPOQ = 1/2 × b × h

= 1/2 × OP × QR

= 1/2 × 12 × 6

= 36 sq cm

Area between the arc PQ and chord PQ = Area of sector - Area of ΔPOQ

= 12π - 36

= 12 ( π-3) sq cm