SOLUTION: Eddie, Ellie and Erwin are playing a game. Eddie is standing 5 m away from the circle while Erwin is on the circle. Ellie draws a line from Eddie to Erwin which is tangent to the c

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Question 1054183: Eddie, Ellie and Erwin are playing a game. Eddie is standing 5 m away from the circle while Erwin is on the circle. Ellie draws a line from Eddie to Erwin which is tangent to the circle. If the distance between Eddie is 10 m away from Erwin, find the radius of the circle.
Answer by ikleyn(52797) About Me  (Show Source):
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Eddie, Ellie and Erwin are playing a game. Eddie is standing 5 m away from the circle while Erwin is on the circle.
Ellie draws a line from Eddie to Erwin which is tangent to the circle. If the distance between Eddie is 10 m away from Erwin,
find the radius of the circle.
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Make a sketch.

Let x = "the radius of the circle".

The tangent to a circle is perpendicular to the radius drawn to the tangent point. It gives an equation

x%5E2+%2B+10%5E2 = %28x%2B5%29%5E2.

Solve for x: x = 7.5.

Right-angled triangle (7.5, 10, 12.5), similar to (3,4,5) right angled triangle.