Archive for the ‘Circles’ Category

Quadrilateral & Circle problem

October 1, 2011 3 comments
medival ideal portrait of Ptolemy

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

September 30, 2011 4 comments

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 .

Solution : Read more…

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.

Solution : Read more…

Categories: Circles Tags: , , ,

Circle problem (2)

September 18, 2011 Leave a comment

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 :

Read more…

Categories: Circles Tags: ,

Circle problem (1)

September 17, 2011 Leave a comment
Categories: Circles, Triangles Tags: , ,
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