The question is from Geometry - Right triangle. It tests our understanding of right triangle properties. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. From before the time, Pythagorus said "Let me call this third thing as Hypotenuse", mathematicians have been enamoured with right triangles.
Question 10: Consider a right–angled triangle with inradius 2 cm and circumradius of 7 cm. What is the area of the triangle?
r = 2
R = 7 (Half of hypotenuse)
Hypotenuse = 14
r = (a + b - h)/2
2 = (a + b - 14)/2
a + b - 14 = 4
a + b = 18
a2 + b2 = 14 2
a2 + (18 - a)2 = 14 2
a2 + 324 + a2 - 36a = 196
2a2 - 36a + 128 = 0
a2 - 18a + 64 = 0
Now the 2 roots to this equation will effectively be a, 18 – a. Product of the roots = 64.
Area = 1/2 * product of roots (How? Come on, you can figure this out.)
= 32 sq. cms
The question is "What is the area of the triangle?"
Choice A is the correct answer.
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