Length of a chord

Geometry Level 2

A chord is perpendicular to the diameter of a circle as shown. Find the length of the chord.

20 20 22 22 18 18 15 15 25 25

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Consider right △ A B C \triangle ABC . By pythagorean theorem, we have

12. 5 2 = ( x 2 ) 2 + 7. 5 2 12.5^2=\left(\dfrac{x}{2}\right)^2+7.5^2

156.25 = x 2 4 + 56.25 156.25=\dfrac{x^2}{4}+56.25

100 ( 4 ) = x 2 100(4)=x^2

400 = x 2 400=x^2

x = 400 = 20 x=\sqrt{400}=\boxed{20}

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