The diagonals of AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that

• AP . CP = BP. DP

• AP. BP = CP. DP

• AP. CD = AB. CP

• BP. AB = CD. CP

N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is

If O be the circumcentre of a Δ PQR and ∠QOR = 110°, ∠OPR = 25° then the measure of ∠PRQ is

• 50°

• 55°

• 60°

• 65°

A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is

• 60 m

• 65 m

• 70 m

• 72 m

A, B, C, D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Then, ∠BAC is

• 90°

• 100°

• 110°

• 120°

In a triangle, if three altitudes are equal, then the triangle is

• equilateral

• right

• isosceles

• obtuse

The tops of two poles of height 24 m and 36 m are connected by wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is

• 8√3 m

• 8 m

• 6√3 m

• 6 m

The value of  is

• cot θ

• cosec θ

• tan θ

• 1

139.

If  then cos θ - sin θ is

• 

• 

• 

• 

If  then  is