Multiple choice

ABC is triangle with side lenghts 13, 14, and 15 units. if is the incentre and R is its circum radius, then the value of $frac{{AI \times BI \times CI}}{R}$ is equal to (in equal to Sq. units)

  1. 130

  2. 64

  3. 126

  4. 100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The triangle has semiperimeter 21 and area 84, so its inradius is 4 and circumradius is 65/8. Using AI = r/sin(A/2), BI = r/sin(B/2), and CI = r/sin(C/2), the product AI × BI × CI divided by R simplifies to 64.

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