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Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm, and PQ = 7 cm, then the diameter (in cm) of the circle is equal to –

SSC · 2024 · Quantitative Aptitude
Question:
Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm, and PQ = 7 cm, then the diameter (in cm) of the circle is equal to –

Options

(1) 26 cm
(2) 13 cm
(3) 12 cm
(4) 24 cm
Answer: (1) 26 cm

Explanation:
Using perpendicular from center bisects chord and Pythagorean theorem, radius = 13 cm, diameter = 26 cm

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