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In a circle of radius 5 cm, two chords AB and AC are drawn from the same point A with AB = AC = 6 cm. Find the length of chord BC.
- 6 cm
- 8 cm
- 9.6 cm
- 12 cm
Correct answer: 9.6 cm
Solution
Place A at the top of the circle. Since AB = AC, BC is perpendicular to the axis of symmetry AO. Using the circumradius relation for triangle ABC: area = (AB*AC*BC)/(4R). Also, by symmetry, the foot of the altitude from A bisects BC. Solving the geometry gives BC = 9.6 cm.
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