Multiple choice general knowledge math & puzzles

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

  1. 26.25

  2. 27.85

  3. 22.45

  4. 32.25
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A Correct answer
Explanation

Using the right triangles ABD and ACD, we find BC = BD + DC. From Pythagoras: BD = sqrt(17.5^2 - 3^2) and DC = sqrt(9^2 - 3^2). This gives BC ≈ 25.725. The circumradius formula R = abc/(4 × Area) with Area = (1/2) × BC × AD yields R = (17.5 × 9 × 25.725)/(4 × 38.588) ≈ 26.25.

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