Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent.

In the XY-plane, the area, in square units, of the region defined by the inequalities $$y \geq x ...

A circular plot of land is divided into two regions by a chord of length $$10\sqrt{3}$$ meters, whi...

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and ...

Let $$ C $$ be the circle $$ x^2 + y^2 + 4x - 6y - 3 = 0 $$, and $$ L $$ be the locus of the point ...

A quadrilateral $$ ABCD $$ is inscribed in a circle such that $$ AB : CD = 2 : 1 $$ and $$ BC : AD ...

A triangle is drawn with its vertices on the circle $$C$$ such that one of its sides is a diameter ...