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A line is tangent to a circle at point A. If a chord AB has length 8 cm and makes an angle of 30° with the tangent, what is the radius of the circle?

1. 4 cm
2. 8 cm
3. 4 \sqrt{3} cm
4. 8 \sqrt{3} cm

Correct answer: 8 cm

Solution

The angle between the tangent and chord equals the angle in the alternate segment, so the chord subtends a 30° angle at the circumference. This gives a triangle where the chord of length 8 cm is opposite a 30° angle, leading to the radius as the circumradius. Using the standard relation, the radius comes out to 8 cm.

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