Two circles intersect at A and B, P is a point on produced BA. PT and PQ are tangents to the circles. The relation of PT and PQ is 

The length of the common chord of two circles of radii 30 cm and 40 cm whose centers are 50 cm apart is (in cm) 

The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that 

ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to 

The distance between the center of two equal circles each of radius 3 cm, is 10 cm. The length of a transverse common tangent is 

A unique circle can always be drawn through x number of given non-collinear points, then X must be 

Two equal circles of radius 4 cm intersect each other such that each passes through the center of the other. The length of the common chord is

The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between there interior angles is 2 : 3. The number of sides of these polygons is respectively