Geomatry

Given an equilateral triangle Tl with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of TI. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the perimeter, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

• 150

• 144

• 132

• 100

In the following figure, it is given that O is the centre of the circle and angle AOC = 140°. Find angle ABC (in degree).

• 110

• 120

• 115

• 130

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

• √10

• √12

• √13

• √15

In a given figure, AABC is circumscribed by a circle having its centre at O. If Oв and OC are the angle bisector of angle B and angle c. Find angle BAC?

• 45

• 60

• 75

• 50

The area of a rectangle is given by A = 8x ^ 2 - 2x - 15 if the length was larger than the breadth, then the length can be

• (3x + 5)

• (5x + 3)

• (4x+5)

• (2x + 3)

Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?

• 1/3

• 1/2

• 2/3

• 5/6

There is a fan with 3 blades at 120° to each other whose central circular disc has an area of 3 cm² and a blade is (20 - sqrt(3)) cm long. If the tips of the blades are joined so as to form a equilateral triangle, what will be the area?

• 900 cm²

• 300√3cm²

• (900+9π) cm²

• (3π+300) cm²

A pond 100m in diameter is surrounded by a circular grass walk-way 2m wide. How many square meters of grass is on the walk way?

• 98π

• 100π

• 202π

• 204π

Two circles with equal radii are drawn, without any overlap, in a semicircle of radius 2cm. If these are largest possible circle that the semicircles accommodate, what is the radius in cm of each circle?

• 0.414

• 0.828

• 0.172

• 0.586

A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ratio of the area of the triangle to the area of the square is

• √3: √2

• 3 √3:2

• 3 : √2

• √2 : 1