For the following questions answer them individually
The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that
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 triangle PQR and $$\angle{QOR} = 110^o, \angle{OPR} = 25^o$$, then the measure of $$\angle{PRQ}$$ is
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
A, B, C, D are four points on a circle. AC and BD intersect at a point such that $$\angle{BEC} = 130^o$$ and $$\angle{ECD} = 20^o$$. Then, $$\angle{BAC}$$ is
The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of 60 $$^{\circ}$$ with the horizontal, then the length of the wire is
If $$\cos\theta + \sin\theta = \sqrt{2}\cos\theta$$, then $$\cos\theta - \sin\theta$$ is
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