# Math Help - Find a radius

An arch over a door is 60 cm high and 200 cm wide, find the radius of a circle containing the arc of the arch. I have included the picture from my book. The answer should be 113.3333 i believe

I have set up the problem

x(60)=100(100) to find the missing part of a chord

and I tried pythag thm

I do not know what else to do Thanks for the help

2. Hello, algebraisabeast!

An arch over a door is 60 cm high and 200 cm wide.
Find the radius of a circle containing the arc of the arch.
Code:
                C
* o *
*     |     *
A o - - - o - - - o B
*     |D    *
*   |   *R
* | *
*
O

The radius of the circle is: $OA \:=\: OB \:=\: OC \:=\: R$

The width of the arch is: $AB \:=\: 200 \quad\Rightarrow\quad AD \:=\: DB \:=\: 100$

The height of the arch is: $CD \:=\: 60.$
. . Hence: $DO \:=\: R -60$

In right triangle $ODB\!:\;\;OD^2 + DB^2 \:=\:OB^2 \quad\Rightarrow\quad (R-60)^2 + 100^2 \:=\:R^2$

So we have: . $R^2 - 120R + 3,\!600 + 10,\!000 \:=\:R^2 \quad\Rightarrow\quad 12R \:=\:13,\!600$

Therefore: . $R \:=\:\frac{13,\!600}{12} \:=\:\frac{3400}{3} \:=\:1133\tfrac{1}{3}$ cm.