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
A.
equilateral
In equilateral triangle, all three altitudes are equal in length.
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