ABCD is a cyclic quadrilateral in which BC = CD and EF is a tangent at A. ∠CBD = 43° and ∠ADB = 62°. Find :

(a) ∠ADC

(b) ∠ABD

(c) ∠FAD

A(a, b), B(-4, 3) and C(8, -6) are the vertices of a △ ABC. Point D is on BC such that BD : DC is 2 : 1 and M(6, 0) is mid-point of AD. Find :

(a) coordinates of point D.

(b) coordinates of point A.

(c) equation of a line parallel to line BC, through M.

The total expenses of a trip for certain number of people is ₹ 18,000. If three more people join them, then the share of each reduces by ₹ 3,000. Take x to be the original number of people, form a quadratic equation in x and solve it to find the value of x.

Using ruler and compass only construct ∠ABC = 60°, AB = 6 cm and BC = 5 cm.

(a) construct the locus of all points which are equidistant from AB and BC.

(b) construct the locus of all points equidistant from A and B.

(c) mark the point which satisfies both the conditions (a) and (b) as P.

Hence, construct a circle with center P and passing through A and B.