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

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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