The chord of the circle is 6√2 dm and contracts the arc 90 degrees find the circumference and the length of the arc.

Given:
circle;
chord = 6 √ 2;
the chord contracts the arc at 90 degrees;
Find: arc length and circumference;

Solution:
If a chord contracts an arc 90 degrees, it follows that it is a side of a square inscribed in a circle.
From the chord formula = R √ 2 we find R /
Substitute the known values, and we get:
6 √ 2 = R √ 2;
R = 6 * √2 / √2;
Reduce the numerator and denominator in the fraction by the root of 6, then we get:
R = 6;
Now let’s find the length of the arc and the length of the circle:
The circumference is C = 2 * 3, 14 * 6 = 37, 68;
The arc length is L = 37, 68/4 = 9, 42.