AB and CD are two parallel chords of a circle such that length of AB and CD are 10 cm and 24cm respectively.if the chords are opposite sides of the centre and the distance between them is 17 cm ,find the radius of the circle.

Answer 1

As usual, draw a diagram. If you draw a line through the center, perpendicular to the chords, you cut them in half. The radius is the hypotenuse of two right triangles. One has a leg of 5, and the other has a leg of 12. So,

5^2 + 12^2 = r^2
12^2 + (17-x)^2 = r^2

5^2 + x^2 = 12^2 + (17-x)^2
x = 12

so, the radius is 13

Answer 2

Draw a diagram,the line from the centre O meet AB at E and CD at F.
Let OF be x then OE = 17-x.
Join AO and OC
In Triangle AOE,
Radius r²= 5² + (17-x)² and
In Triangle COF,
Radius r²= 12² + x² then
12² + x²= 5² + (17-x)²
144 + x² = 25 + 289 -34x + x²
34x + x² - x² = 314 - 144
34x = 170
x = 5
So, r² = 12² + 5²
r² = 144 + 25
r² = 169
r = 13 cm /-