# CAT Practice : Geometry-Triangles

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From before the time, Pythagorus said "Let me call this third thing as Hypotenuse", mathematicians have been enamoured with right triangles

## Right triangle properties

Q.10: Consider a right–angled triangle with inradius 2 cm and circumradius of 7 cm. What is the area of the triangle?
1. 32 sq cms
2. 31.5 sq cms
3. 32.5 sq cms
4. 33 sq cms

Choice (A). 32 sq cms

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## Detailed Solution

r = 2
R = 7 = ${({1 \over 2} of hypotenuse)}$
Hypotenuse = 14
r = ${{a + b −h} \over 2}$
2 = ${{a + b −14} \over 2}$
a + b – 14 = 4
a + b = 18
a2 + b2 = 142
a2 + (18 – a)2 = 196
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 = ${1 \over 2}$ × product of roots (How? Come on, you can figure this out.)
= 32 sq. cms

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.