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
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°
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
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°
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
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
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 60o and 30o, respectively. Find the height of the balloon above the ground.
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.