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dout
Asked by satnamk123 | 15 Apr, 2024, 01:50: AM
Expert Answer
Figure shows a circle whose origin is at center passes through an equilateral triangle ABC .
Median of triangle is AD = ( 3 a ) and median passes through origin .
ΔBAD is right triangle having angles 90°, 60° and 30°.
Hence if AD = 3a , then AB = ( 2√3 a ) .............................(1)
( use the property of right triangle having angles 90°, 60° and 30° have sides in the ratio 2 : √3 : 1 ) .
In the ΔAOB , ∠AOB = 120° . Let OA = OB = r is radius of circle.
Then by cosine rule ,
Using eqn.(1) and above expression , we get
√3 r = 2 √3 a
Hence radius r of circle is 2a .
If centre of circle is at origin and radius is 2a , then
x2 + y2 = (2a)2 = 4a2
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