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AP EAMCET · Maths · Properties of Triangles

If \(R=\frac{65}{8}, r_1=\frac{21}{2}\) and \(r_2=12\) are the circum radius, radii of the excircles opposite to the vertices \(A\) and \(B\) of a triangle \(A B C\) respectively, then the area of the triangle (in square units) is

  1. A \(\frac{2}{3}\)
  2. B 28
  3. C 84
  4. D 168
Verified Solution

Answer & Solution

Correct Answer

(C) 84

Step-by-step Solution

Detailed explanation

\(\Delta = r_1 r_2 \sqrt{\frac{4R - (r_1+r_2)}{r_1+r_2}}\) \(\Delta = \left(\frac{21}{2}\right) (12) \sqrt{\frac{4\left(\frac{65}{8}\right) - \left(\frac{21}{2}+12\right)}{\frac{21}{2}+12}}\) \(\Delta = 126 \sqrt{\frac{\frac{65}{2} - \frac{45}{2}}{\frac{45}{2}}}\)…