# How to calculate the distance of the circumcenter to one of the sides of a triangle inscribed in a circle?

In a triangle $ABC$, the $∠A = 53 °$ and the circumference measures $20$, calculates the double of the distance to the $\overline{BC}\quad$side.

I do not understand the question why it asks for the distance of the circumcision to the $\overline{BC}\quad$side, and this distance varies according to the point on the $\overline{BC}\quad$side of the triangle. On the other hand, if it would be the distance from the cicuncentro to one of the points between $B$ and $C$ of the circumference, it would be $40$ ... But the answer is $24$.

Circunference

• Did you mean the radius is 20? Jul 30, 2018 at 17:51

Let $O$ be a center of the circle and $OD$ be a perpendicular from $O$ to $BC$.

I think it means to find $2OD$.

Since $$\measuredangle COD=\frac{1}{2}\measuredangle BOC=53^{\circ},$$ we obtain: $$2OD=2\cdot20\cos53^{\circ}=24.07...$$

• Excuse me it was my mistake, they asked me twice the distance of the circumcenter to the $\overline{BC}\quad$ side.
– Payo
Jul 30, 2018 at 16:25
• @Payo It's exactly, which I got. Jul 30, 2018 at 16:26
• @Michael- My mistake Jul 30, 2018 at 16:30
• Yes, Thank you @Michael
– Payo
Jul 30, 2018 at 16:40
• You are welcome! Jul 30, 2018 at 17:26