### Archive

Archive for the ‘Circles’ Category

Image via Wikipedia

Quadrilateral ABCD is inscribed in a circle. Let AB = a, BC = b, CD = c, DA = d, AC = p and BD = q. Prove Ptolemy’s second theorem that $p \cdot q = \frac{ad+bc}{ab+cd}$ .

This question is also taken from Bertley Math Circle .

It is easy question, just use $R = \frac{abc}{4S}$ a, b, c are sides of triangle and S is area of triangle.

If you couldn’t prove send me mail, and i will give few tips.

## Triangle – Circle problem

Given triangle ABC. $\angle C = 90^\circ$ . CD is height of triangle ( point D is on hypotenuse AB ). The radiuses of incircles of triangles ACD and ABD are $r_1 \: and \: r_2$ . Find the radius of incircle of triangle ABC .

## Circle of grass

September 28, 2011 1 comment

There is a circle of grass with the radius R. We want to let a sheep eat the grass from that circle by attaching the sheep’s leash on the edge of the circle. What must be the length of the leash for the sheep to eat exactly half of the grass?

This question is taken from physicsforum.

Categories: Circles Tags: , , ,

## Circle problem (2)

Radiusları Rr olan iki çevrə xarici toxunandır. Bu çevrələrə və bu çevrələrin xarici toxunanına toxunan çevrənin radiusunu tapın.

Given two circles (O1,r) & (O2,R). Find the radius of third circle (O3) .

# Solution :

Categories: Circles Tags: ,

## Circle problem (1)

$\vartriangle ABC is \: equilateral. Proof \: that, DA=DC+DB .$