ABC is an isosceles triangle inscribed in a circle if ab is equal to AC is equal to 12 root 5 cm and BC is equal to 24 cm find the radius of the circle
Answers
Radius of the circle = 15 cm if ABC nscribed in a circle AB = AC = 12√5 cm & BC = 24 cm
Step-by-step explanation:
BC² = AB² + BC² - 2AB. BC Cos∠A
=> 24² = (12√5)² + (12√5)² - 2 (12√5) (12√5)Cos∠A
=> 576 = 720 + 720 - 1440Cos∠A
=> Cos∠A = 864/1440
=> Cos∠A = 3/5
=> ∠A = Cos⁻¹(3/5)
Angle subtended by chord BC = A = Cos⁻¹(3/5)
Angle subtended by BC at center = 2A
in Δ BOC
BO = CO = R = Radius
BC = 24 cm
BC² = BO² + CO² - 2BO * CO Cos(2A)
=> 24² = R² + R² - 2R²Cos(2A)
=> 576 = 2R²(1 - Cos2A)
=> 288 = R² ( 1 - (2Cos²A - 1))
=> 288 = R² (2 - 2Cos²A)
=> 144 = R² (1 - Cos²A)
=> 144 = R² ( 1 - (3/5)² )
=> 144 = R² (16/25)
=> R² = 25 * 9
=> R = 5 * 3
=> R = 15
radius of the circle = 15 cm
Learn more:
An equilateral triangle is inscribed in a circle of radius 7 cm. Find the ...
https://brainly.in/question/10153152
a circle with Centre P is inscribed in a triangle ABC side a b side BC ...
https://brainly.in/question/8756941