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An equilateral triangle is drawn inside a square What is the value of the angle in degrees?

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Important Questions on Taste of The Exams - Block IV
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In a triangle the lengths of the sides and AC equal and respectively. Let be a point on the line segment such that is perpendicular to If then what is the radius (in ) of the circle circumscribing the triangle

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Consider obtuse-angled triangles with sides and If is an integer then how many such triangles exist?

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Consider a square with midpoints of and respectively. Let denote the line passing through and Consider points and on and inside such that the angles and both equal What is the ratio of the area of to the remaining area inside

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Two circles, both of radii intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq. .) of the intersecting region?

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Consider a right circular cone of base radius and height A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq. ) of the cylinder.

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From a triangle with sides of lengths and a triangular portion is cut off where is the centroid of The area, in sq. of the remaining portion of triangle is

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Let be a right-angled isosceles triangle with hypotenuse Let be a semi-circle, away from with diameter Let be an arc of a circle centered at and lying between and If has length then the area, in of the region enclosed by and is

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A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
