Multiple choice

If the length of two chords AB and AC of a circle is 8 cm and 6 cm, respectively and ∠BAC = 90o, then the radius of the circle is

  1. 5 cm

  2. 6 cm

  3. 4 cm

  4. 8 cm

  5. None of these
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A Correct answer
Explanation

Since angle BAC is 90 degrees, the chord BC must be the diameter of the circle. Using the Pythagorean theorem, the diameter BC = sqrt(8^2 + 6^2) = sqrt(64 + 36) = 10 cm. The radius is half the diameter, which is 5 cm.

AI explanation

Since angle BAC is 90 degrees, BC must be the diameter of the circle. Using the Pythagorean theorem, the diameter BC equals the square root of (8^2 + 6^2), which is the square root of 100, or 10. The radius is half of the diameter, so it is 5 cm. The result is 5 cm.

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