If C₁, C₂ be the centres of rwo circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.

Angle subtended by a chord AB on the centre of the circle is 140 degree. What will be the angle subtended by the chord AB on the major are of the circle? 

ABCD is a cycle quadrilateral and BC is diameter of the related circle on which A and D also lie. ∠BCA =19⁰ and ∠CAD=32⁰. What is the measure of ∠ACD?

In the figure, XYZ is a secant. and ZT is a tangent to the circle at T. If TZ = 12 cm and YZ = 8 cm, then find the length of XY.

In ΔABC, if G is the centroid and AD is a median with length 9 cm, then the length of AG is:

If in a triangle, the circumcenter, incentre, centroid and orthocenter coincide, then the triangle is

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then.

ABC is a triangle in which DE || BC and AD: DB = 5: 4. Then DE: BC is