1. If a triangle is inscribed in a circle of radius 30.5 cm with integer sides 11, 61 and x. Find x
(A) 51
(B)55
(C)54
(D) None of these
Answers
Given : a triangle is inscribed in a circle of radius 30.5 cm with integer sides 11, 61 and x
To find : x from given options : (A) 51 , (B)55 , (C)54 , (D) None of these
Solution:
Radius of Circle = 30.5 cm
Diameter of circle = 2 * Radius = 2 * 30.5 = 61 cm
One Side of Triangle is 61 cm
Hence one side of triangle is Diameter
Hence Triangle is right angle triangle with 61 cm Side as hypotenuse
Another Side = 11 cm
Third side = x cm
x² = 61² - 11²
=> x² = (61 + 11)(61 - 11)
=> x² = 72 * 50
=> x² = 36 * 2 * 2 * 25
=> x² = 6² * 2² * 5²
=> x² = 60²
=> x = 60
Hence none of these is correct option
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