Multiple choice

The in-radius of the triangle of maximum area inscribed in a circle of radius 46 cm is

  1. 46

  2. 23

  3. 92

  4. 45
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B Correct answer
Explanation

For a circle of radius R, the triangle of maximum area inscribed is an equilateral triangle. The side length of this triangle is R*sqrt(3), and its in-radius r is given by R/2. Given R=46, the in-radius is 46/2 = 23.

AI explanation

The triangle of maximum area inscribed in any circle is an equilateral triangle. If the circumradius is R = 46 cm, the relation between the circumradius and the inradius (r) of an equilateral triangle is r = R/2. Substituting the given circumradius gives r = 46/2 = 23 cm.

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