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Geometry and Trigonometry Question Solving - 18 July

1. A solid is hemispherical at the bottom and conical above. If the surface area of the two parts are equal,then the ratio of its radius and height of its conical part will be - 2. From a tower 125 metres high, the angle of depression of 2 objects, which are in horizontal line through the base of the tower, are 45 degree and 30 degree and they are on the same side of the tower. The distance between the objects is - 3. The perimeter of a rectangle and a square is 120 metres each. The area of the rectangle is less than the area of the square by 100 square metre. Then the length of the rectangle is 4. The vertex of an isosceles triangle measure 10 times the measure of the base angle. Find the measure of the base angle.

5. PQRS is a rhombus whose three vertices P, S & R lie on the same circle while the fourth vertex Q lies on its centre. If the area of the rhombus is 8root3 square cm. What is the radius of the circle? 6. C & D are two points on a semicircle subscribed on BA as diameter. If Angle BAD = 40 degree, Angle DBC = 20 degree, then what is the value of the Angle ABD ? 7. If the base of a triangle is doubled and the height becomes 4 times the initial value, then by what percentage does the area of the circle increases ?

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