In a circle, there are two parallel chords of lengths 10 cm and 24 cm. Both chords are situated on the same side of the center. If the distance between them is 7 cm, find the area of the circle.
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Correct answer: A
Explanation
Given:
First chord = 10 cm
Second chord = 24 cm
Distance between the two = 7 cm
Formula:
Distance of chord from the center = √(r² − (c/2)²)
Distance for the first chord = √(r² − 5²)
Distance for the second chord = √(r² − 12²)
√(r² − 25) − √(r² − 144) = 7
Squaring both sides:
(r² − 25) + (r² − 144) − 2√[(r² − 25)(r² − 144)] = 49
2r² − 169 − 2√[(r² − 25)(r² − 144)] = 49
2√[(r² − 25)(r² − 144)] = 2r² − 218
Then solving by squaring,
r² = 169
r = 13
Area of the circle = πr² = π × 169 = 169π cm²