Multiple choice

Four tangents drawn to a circle intersect each other to form a quadrilateral. The lengths of 3 consecutive sides are 6 cm, 10 cm and 16 cm. Find the length of the fourth side.

  1. 12 cm

  2. 9 cm

  3. 7 cm

  4. Data inadequate
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A Correct answer
Explanation

For a quadrilateral circumscribed about a circle, the sums of opposite sides are equal. Let the sides be a, b, c, d in order. Then a + c = b + d. Here, 6 + 16 = 10 + d, so 22 = 10 + d, which means d = 12.

AI explanation

By the property of tangents drawn from an external point to a circle, the lengths of the two tangent segments from a vertex are equal. Let the unknown fourth side be x; the tangent segments alternate around the quadrilateral. Setting the sums of opposite sides equal, 6 + 16 = 10 + x, which simplifies to 22 = 10 + x.

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