Question

as a part of a compaign , a huge balloon with message of awarenesd of cancer was displayed from the terrace of a tall building . it was held by string of lenght 8 m each , which inclined at an angle of 60 at the point , where it was tiedas shown in figure .
what is the lenght of AB
if the perpendicular drawn from the centre of the circle to the chord is 3 cm find the radius of circle .​

Answer 1

length of AB = 8 m & the radius of circle = 5 m

Step-by-step explanation:

PA = PB = 8 m

∠APB = 60°

AB² = PA² + PB² - 2PA*PBCos∠APB

=> AB² = 8² + 8² - 2 * 8*8Cos60

=> AB² = 8² + 8² - 2 * 8*8(1/2)

=> AB² = 8² + 8² - 8²

=> AB² = 8²

=> AB = 8 m

length of AB = 8 m

Let say Radius of Circle = R  m

OM ⊥ AB & OM = 3 m

AM = BM = AB/2 = 8/2 = 4 m

OA² = AM² + OM²

=> R² = 4² + 3²

=> R² = 16 + 9

=> R² = 25

=> R = 5

the radius of circle = 5 m

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