A point `P` is given on the circumference of a circle of radius `rdot` Chords QR are parallel to the tangent at `Pdot` Determine the maximum possible area of triangle PQR.

From a fixed point A on the circumference of a circle of radius r , the perpendicular A Y falls on the tangent at Pdot Find the maximum area of triangle A P Ydot

Rectangles are inscribed inside a semi-circle of radius rdot Find the rectangle with maximum area.

PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

AB is a diameter of a circle and C is any point on the circumference of the circle. Then (a) the area of DeltaABC is maximum when it is isosceles (b) the area of DeltaABC is minimum when it is isosceles (c) the perimeter of DeltaABC is minimum when it is isosceles (d) none of these

Pa n dQ are two points on a circle of centre C and radius alpha . The angle P C Q being 2theta , find the value of sintheta when the radius of the circle inscribed in the triangle C P Q is maximum.

Tangents are drawn from external point P(6,8) to the circle x^2+y^2 =r^2 find the radius r of the circle such that area of triangle formed by the tangents and chord of contact is maximum is (A) 25 (B) 15 (C) 5 (D) none of these

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR

Fill in the blanks (i) A tangent to a circle touches it in …... Point (s). (ii) A line intersecting a circle in two points is called a ….. (iii) Number of tangents can be drawn to a circle parallel to the given tangent is …. (iv) The common point of a Tangent to a circle and the circle is called ..... (v) We can draw ..... tangents to a given circle. (vi) A circle can have ..... parallel tangents at the most.