problem archive
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From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45°... -
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the... -
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of ... -
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the... -
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of th... -
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determi... -
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly b... -
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the ballo... -
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is appr... -
A car is moving towards a tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by... -
On a paper, draw a circle and a secant PQ of the circle. Draw various lines parallel to the secant on both sides of it. You will find that after some ... -
How many tangents can a circle have? -
Fill in the blanks: (i) A tangent to a circle intersects it in _______ point(s). (ii) A line intersecting a circle in two points is called a _______. ... -
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is: (A) 12 cm (B) 13... -
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle. -
Draw a circle on a paper. Take a point P inside it. Can you draw a tangent to the circle through this point? You will find that all the lines through ... -
Next take a point P on the circle and draw tangents through this point. You have already observed that there is only one tangent to the circle at such... -
Finally, take a point P outside the circle and try to draw tangents to the circle from this point. What do you observe? You will find that you can dra... -
Note that in Fig. 10.6 (iii), PT_1 and PT_2 are the lengths of the tangents from P to the circle. The lengths PT_1 and PT_2 have a common property. Ca... -
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.