A chord AB of length 16 is drawn in a circle with a radius of 4 roots of 5. Find the distance from the center

A chord AB of length 16 is drawn in a circle with a radius of 4 roots of 5. Find the distance from the center of the circle to the chord.

The center of the circle O and Chord AB, form a triangle ABO, where AB is the base, OB and OA are the lateral sides, they are the radii of the circle. ОВ = ОА, means triangle ABO, isosceles.
Let us draw from point O the height OH of the ABO triangle. The height dropped from the top of an isosceles triangle divides the base into 2 equal parts:
BО = ОА = 16/2 = 8
Consider a triangle AOH, AO = 4√5, AH = 8, <OHA = 90 °, by the property of the triangle’s height. Let’s use the Pythagorean theorem:
AO² = OH² + AH²
Let us express OH from this expression:
OH = √ (AO²-AH²) = √80-64 = 4
Answer: the distance from the center of the circle to the chord 4.