Multiple choice

ABC is an equilateral triangle inscribed in a circle with AB = 5 cm. Let the bisector of angle A meet BC in X and the circle in Y. What is the value of AX.AY?

  1. 16 cm2

  2. 20 cm2

  3. 25 cm2

  4. 30 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In an equilateral triangle inscribed in a circle, the product of the segments of a chord (or secant) is constant. AX is the altitude (5 * sqrt(3) / 2) and XY is the remaining part of the diameter. Using properties of chords, AX * AY = AB * AC = 5 * 5 = 25.

AI explanation

By the intersecting chords theorem, the product of the lengths of the two segments of one chord equals the product of the segments of the other chord, meaning AX * AY = AB * AC. Because ABC is an equilateral triangle, both AB and AC are 5 cm. Multiplying these gives AX * AY = 5 * 5 = 25 cm^2.

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