From the top of vertical tower, the angle of depression of two cars, in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [Use = 1.73]

Point P(x, 4) lies on line segment joining the points A(-5, 8) and B(-4, 10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

Find the area of the quadrilateral ABCD, whose vertices are A(-3, -1), B(-2, -4), C(4, -1) and D(3, 4)

OR

Find the area of triangle formed by joining the mid-points of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is 12.

OR

A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

Prove that the tangents at any point of a circle is perpendicular to the radius through the point of contact.