Forum

Circles

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(A) 60 cm² (B) 65 cm²       (C)  30 cm² (D) 32.5 cm²

Circles

In Fig. , AB is a chord of the circle and  AOC is its diameter such that  ∠ACB  =  50°.  If AT  is  the tangent to the circle at the point  A, then ∠BAT is equal to

(A) 65° (B) 60° (C) 50° (D) 40°

Circles

In  Fig. ,  if ∠AOB  =  125°, then ∠COD is equal to

(A) 62.5° (B) 45° (C) 35° (D) 55°

Circles

If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
(A) 3 cm (B) 6 cm (C) 9 cm (D) 1 cm

Circles

In  Fig., PQ  is  a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is equal to 

(A) 135° (B) 150° (C) 120° (D) 110°

Circles

In  Fig. ,  the  pair  of AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is

(A) 10 cm (B) 7.5 cm (C) 5 cm (D) 2.5 cm

Circles

If angle between two radii of a circle is 130º, the angle between the tangents at the ends of the radii is :

(A) 90º (B) 50º  (C) 70º (D) 40º 

Introduction to Trignometry & its Equation

The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation  of  a  balloon  from  these  windows  are  observed  to  be  60^o and  30^o, respectively. Find the height of the balloon above the ground.

Introduction to Trignometry & its Equation

A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β,  respectively. Prove that the height of the other house is h ( 1 + tan α  cot β ) metres.

Introduction to Trignometry & its Equation

The angle of elevation of the top of a vertical tower from a point on the ground is 60^o . From another point 10 m vertically above the first, its angle of elevation is 45^o. Find the height of the tower.