Mind Warmups-6

Geometry Level 3

In the figure above, the rectangle at the corner measures 10×20. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle?

50 10 40 30

Sanjeet Raria by Sanjeet Raria , 27, India

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1 solution

Rudresh Tomar
Aug 24, 2014

B y p y t h a g o r a s t h e o r e m : ( x − 10 ) 2 + ( x − 20 ) 2 = x 2 ( x − 10 ) ( x − 50 ) = 0 x ≠ 10 ∴ x = 50 By\quad pythagoras\quad theorem:\\ { (x-10) }^{ 2 }+{ (x-20) }^{ 2 }={ x }^{ 2 }\\ (x-10)(x-50)=0\\ x\quad \neq \quad 10\\ \therefore \quad x=50

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