Question

Two parallel chords of lenght 24cm and 10cm which lie on opposite sides of the circle are 17cm apart.calculate the radius of the circle to the nearest whole number.

Answer 1

Did you make your sketch?

Let the distance from the longer chord to the circle be x
then the distance from the shorter chord to the circle is 17-x
Let the radius be r

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

so x^2 + 144 = (17-x)^2 + 25

x^2 + 144 = 289 - 34x + x^2 + 25
34x = 170
x = 5

then r^2 = x^2 + 12^2
r^2 = 25+144 = 169

r = √169 = 13

Answer 2

Two parallel chord of length 24cm and 10 cm which lie on opposite sides of a circle to the nearest whole number