Circles

In the XY-plane, the area, in square units, of the region defined by the inequalities $$y \geq x + 4 $$ and $$ -4 \...

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

A quadrilateral $$ ABCD $$ is inscribed in a circle such that $$ AB : CD = 2 : 1 $$ and $$ BC : AD = 5 : 4 $$. If $$ AC...

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

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y , are drawn such t...

A rectangle with the largest possible area is drawn inside a semicircle of radius $$ 2 \, \text{cm} $$. Then, the ratio...

All the vertices of a rectangle lie on a circle of radius $$ R $$. If the perimeter of the rectangle is $$ P $$, then t...

In a triangle ABC, $$AB = AC = 8$$ cm. A circle drawn with $$BC$$ as diameter passes through $$A$$. Another circle drawn...

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