Multiple choice

In a triangle ABC, bisector of angle C meets the side AB at D and circumcentre at E. The maximum value of CD. DE is equal to

  1. $a^2 /4$
  2. $b^2 /4$
  3. $c^2 /4$
  4. $(a + b)^2/4$
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C Correct answer
Explanation

In a triangle, the product of the segment of the angle bisector (CD) and the segment from the bisector to the circumcircle (DE) is related to the sides of the triangle. By the power of a point theorem, CD * DE = AD * DB. For a triangle, this product is maximized as c^2 / 4.

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