In a circle with center O, two parallel chords GH and IJ are on opposite sides of the center. The length of chord GH is 24 cm and the length of chord IJ is 10 cm. If the distance between the two chords is 17 cm, what is the diameter of the circle?
Show answer & explanation
Correct answer: B
Explanation
Given:
GH = 24 cm
IJ = 10 cm
Distance between the two chords = 17 cm
According to the formula:
(Half-chord)² + (Distance from center)² = Radius²
GH/2 = 12
Let the distance of GH from the center be x
Distance of IJ from the center = 17 − x
Radius² = 12² + x² = 144 + x²
For the second chord:
Radius² = 5² + (17 − x)²
= 25 + (17 − x)²
144 + x² = 25 + (17 − x)²
144 + x² = 25 + 289 − 34x + x²
144 = 314 − 34x
34x = 170
x = 5
Radius² = 144 + 25 = 169
Radius = 13
Diameter = 26 cm