# CAT Practice : Coordinate Geometry

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Very simple Question!! Go about it by focussing on the radius of the circle or side of the Triangle.

## Ratio of Areas

Q.27: Consider equilateral triangle T inscribed in circle C, what is ratio of the areas of T and C? Consider Circle C inscribed in equilateral triangle T, what is ratio of the areas of T and C?
1. 3${\surd 3}$ : ${\Pi}$ , 3${\surd 3}$ : ${16\Pi}$
2. 3${\surd 3}$ : ${4\Pi}$, 3${\surd 3}$ : ${\Pi}$
3. ${\surd 3}$ : ${\Pi}$ , 3${\surd 3}$ : ${4\Pi}$
4. ${\surd 3}$ : ${\Pi}$ , ${\surd 3}$ : ${16\Pi}$

Choice (B). 3${\surd 3}$ : ${4\Pi}$, 3${\surd 3}$ : ${\Pi}$

## Detailed Solution

For any equilateral triangle of side ‘a’:
Inradius = ${\frac {a}{2√3} }$ and circumradius = ${\frac {a}{√3} }$

Area of equilateral triangle = ${\frac {√3}{4}}$ * a2

Area of smaller circle = ${\pi * \frac {a}{2√3} * \frac {a}{√23}}$

Area of larger circle = ${\pi * \frac {a}{√3} * \frac {a}{√3}}$

When Equilateral triangle T inscribed in circle C,
Ratio of Areas of T and C :: 3${\surd 3}$ : ${4\Pi}$

When Circle C inscribed in equilateral triangle T,
Ratio of Areas of T and C :: 3${\surd 3}$ : ${\Pi}$

Correct Answer: (B). 3${\surd 3}$ : ${4\Pi}$, 3${\surd 3}$ : ${\Pi}$

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## More questions from Geometry Triangles

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.