alleryIn a circle of radius 7 cm, a tangent and a chord meet at the point of contact with an angle of 60 degrees. The length of the chord is
A7 (square root of 3) cm
B7 cm
C14 cm
D7/2 cm
Answer & Solution
Correct answer: A. 7 (square root of 3) cm
1. Tangent-chord angle 60 means central angle 2 × 60 = 120 degrees subtended by chord.
2. Chord squared = 2 r squared (1 - cos(120)) = 2 × 49 × 3/2 = 147.
3. Chord = square root of 147 = 7 (square root of 3) cm.
_Source: syllabus Mathematics, Ch 10 "Circles", §10.3_
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