SOLUTION: Two chord 10cm and 24cm lies on the opposite side of a circle.The distance between them is 17cm.find the radius of the circle.

Question 978870: Two chord 10cm and 24cm lies on the opposite side of a circle.The distance between them is 17cm.find the radius of the circle.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Draw this figure as a graph.

Use cartesian system, and form a circle centered at the origin, (0,0). Show two parallel cords, each on opposite halves of the center. One cord is 10 units length above the origin and parallel to x-axis. Other cord is 24 units and is below the center and parallel to x-axis.

y-axis cuts the two cords in halves, so there is x coordinate 5 units to the right for the upper cord and x coordinate 12 units to the right for the lower cord. Call the 5 unit part corresponding to vertical coordinate y sub 1, and the 12 unit x coordinate part corresponding to vertical coordinate y sub 2.

The two cords are given as 17 units apart, so then .

You should also be able now to identify two points ON the circle:
(5,y_sub_1) and (12, y_sub_2).

The distance from (0,0) to each of those two points is the radius, so equal for both these distances. Be aware, you can use Pythagorean Theorem here: radius r, x-coordinate, y-coordinate.

Although this could need a good lengthy bit of algebra, you should be able to form the system:
r, for radius,

which is three equations in three unknowns.

A possible good strategy is to first equate the two expressions for r^2, and use the "17" equation to eliminate one of the y subscripted variables, and solve for the other; then find the other subscripted y's. Use either or both to finally evaluate r.
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Trying this strategy myself, y_sub_1 is 12, y_sub_2 is 5;
and r=13.
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