# Tends to infinity

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## A Geometrical construction

Posted by tendstoinfinity on January 25, 2011

pichak@scientist.com

## An easy challenge  ” Draw a circle of radius r centered at A and another  point C is given. Draw a line through C so that chord cut off by circle along this line is of length d“

I request you to try on your own first then see my solution.  you can have better solution than me. if you got another one pl. share.

First this simple geometrical construction ” A circle is given and a point B outside it. Draw a tangent to the circle through B.”   You, I hope will be able to draw the required construction.

Draw the circle “c” with centre A and the point B. Join the points A and B. Bisect the line segment AB at C. draw a circle “d” with centre C and radius BC. let the circle “d” intersects circle “c” at D.
the line through B and D will be required tangent.

Now the original construction

Draw the given circle “c” with radius r centered at A

Draw another circle “d” concentric with the given circle with radius $\sqrt{r^{2}-d^{2}/4}$

draw the tangent through C to d. this line will cut a chord of length d of circle “c”

hope the construction is justified by you. Again a  challenge to you which I will solve in another post.