A chord of a circle of radius 12 cm. subtends an angle of 120° at the centre. Find the area of the corre- sponding minor segment of the circle (use r = 3.14 and V3 = 1.732) 1.
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Answer:
88.44 CM²
Step-by-step explanation:
Area of minor segment = Area of sector OAPB - Area of triangle AOB
Area of segment OAPB = θ/360 × πr²
= 120/360 × 3.14 ×12 ×12
= 3.14 × 4 × 12
= 150.72 cm²
Area of Triangle AOB = 1/2 × base × height
Draw OM Perpendicular to AB
△ OMA ≅ △ OMB (RHS CONGRUENCY)
∠AOM = ∠BOM (CPCT)
∠AOM = ∠BOM = 1/2 × AOB
= 1/2 × 120 = 60°
AM = BM = 1/2 AB
IN △ OAM
SIN 60 = AM/12
AM = 6√3 CM
AB = 2 × 6√3 = 12√3 CM
Area of AOB = A/4 √4B² - A²
= 12√3 / 4 × √(4(12)²- (12√3)
= 3√3 × √144 (4-3)
= 3√3 × 12 = 36√3 CM²
Area of Minor segment APB = 150. 72 - 36√3
= 150.72 - 62.28 = 88.44 CM²
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