Multiple choice

(\text{In }\triangle ABC, \angle B = 90^{\circ}\text{ and AC is the hypotenuse. D is its circumcenter, and } AB = 3 \text{ cms, } BC = 4 \text{ cms. Find the value of BD.})

  1. 3 cm

  2. 4 cm

  3. 5 cm

  4. 2.5 cm
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D Correct answer
Explanation

In a right triangle, the circumcenter is the midpoint of the hypotenuse. For triangle ABC with angle B = 90°, AC is the hypotenuse. AC = sqrt(3² + 4²) = 5 cm by Pythagoras theorem. The circumcenter D is the midpoint of AC, so BD = half of AC = 5/2 = 2.5 cm. This is the circumradius of a right triangle.

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