1.  The area of the largest triangle that can be inscribed in a semi-circle of radius r, is :

r2
2r2
r3
2r3

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Answer: Option  A Explanation:Required area = 1⁄2 * base * height = (1⁄2 * 2r * r) = r2. ```

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2.  An equilateral triangle, a square and a circle have equal perimeters. If T denotes the area of the triangles, S the area of the square and C, the area of the circle, then :

S < T < C
T < C < S
T < S < C
C < S < T

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Answer: Option  D Explanation:Let the perimeter of each be a.
Then, side of the equilateral triangle = a⁄3; side of the square = a⁄4
radius of the circle = a⁄2π.
T = $\sqrt{3}$⁄4 * (a⁄3)2 = $\sqrt{3}$a2⁄36;
S = (a⁄4)2 = a2⁄16;
C = π * (a⁄2π)2 = a2⁄4π = 7a2⁄88.
So, C > S > T. ```

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3.  Formula for a Radius of incircle of an equilateral triangle of side a ?

a2$\sqrt{2}$
a2$\sqrt{3}$
a3$\sqrt{2}$
a3$\sqrt{3}$

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4.  Formula for area of a equilateral triangle

$\sqrt{3}$4 * (side)2
$\sqrt{2}$4 * (side)2
$\sqrt{3}$4 * (side)3
$\sqrt{3}$2 * (side)2

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5.  The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its incircle is :

3$\sqrt{2}$ cm
4$\sqrt{2}$5 cm
5$\sqrt{2}$4 cm
6$\sqrt{2}$

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Answer: Option  C Explanation:We have : a = 6, b = 11, c = 15, s = 1⁄2(6 + 11 + 15) = 16.
Area of the triangle , △ = $\sqrt{\mathrm{16 * 10 * 5 * 1}}$ = 20$\sqrt{2}$ cm2.
Radius of incircle =△⁄s = 20$\sqrt{2}$⁄16 = 5$\sqrt{2}$⁄4 ```

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