Circle of Midpoints of Secants

Geometry Level 4

Consider the circle x 2 + y 2 = 25 x^2 + y^2 = 25 , and a point A ( 1 , 2 ) A (1, 2) lying inside it. Next consider secants of the circle passing through point A A . It turns out that the midpoints of the secants, lie on another circle of center ( a , b ) (a, b) and radius r r .

Find the triplet ( a , b , r ) (a, b, r) .

Inspiration .

( 1 , 2 , 5 ) (1, 2, 5) ( 1 , 2 , 5 ) \left (1, 2, \sqrt{5}\right ) ( 1 2 , 1 , 5 2 ) \left (\frac{1}{2} , 1, \frac{\sqrt{5}}{2}\right ) ( 0 , 0 , 5 ) \left ( 0, 0, \sqrt{5}\right )

Hosam Hajjir by Hosam Hajjir , 56, Canada

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1 solution

Ahmad Saad
Jan 30, 2017

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