#### A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA

#### Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

#### A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.

#### If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

#### Find the value of p, for which one root of the quadratic equation px^{2} – 14x + 8 = 0 is 6 times the other.

#### For what value of n, are the nth terms of two A.Ps 63, 65, 67,... and 3, 10, 17,... equal?