Question

How do you find the radius of the circumscribed circle?

Answer 1

`12`

Explanation:

In a circle, the line joining the center of the circle to the mid-point of a chord is perpendicular to the chord.

Given that `D,E,F` are the midpoint of chords `AB,AC,and BC`, and `OD,OE,and OF` are perpendicular to chords `AB,AC, and BC`, respectively, `=>` point `O` is the center of the circumscribed circle.
In other words, the three perpendicular bisectors of `AB,AC, and BC` meet at point O, `=>` point `O` is the center of the circumscribed circle.

`=> OA, OB =` the radius of the circle
`=> OA=OB`
Given that `OA=5x-8, and OB=3x`,
`=> 5x-8=3x`
`=> x=4`
`=> OA=OB=3x=3*4=12`
Hence, the radius of the circumcircle `=12`