Geometry Practice : Circumradius

This aptitude question is geometry problem solving question. Concept tested: Properties of right triangles; how to compute the radius of the circumscribing circle of triangle whose sides are given.

Question

What is the circum radius of a triangle whose sides are 7, 24 and 25 respectively?

1. 18
2. 12.5
3. 12
4. 14

  Correct Answer      Choice (2). The circumradius of the triangle measures 12.5 units

Explanatory Answer

7, 24, 25 is a Pythagorean triplet. Therefore, the given triangle is a right angled triangle.

In a right-angled triangle, the circum radius measures half the hypotenuse.
The hypotenuse of the given triangle is 25. ∴ its circum radius is 12.5 units

Additional Property: The median to the hypotenuse will also be equal to half the hypotenuse and will measure the same as the circumradius.

  The correct answer is Choice (2).