The radius of the circle is 5 cm. Find the distance from the center of the circle to the line containing the chord equal to 8 cm.
| August 3, 2021 | education
The length of the chord AB = 8 cm.From the center of the circle, point O, we draw the radii OA and OB, the length of which is 5 cm.
The AOB triangle is isosceles.
The distance from point O is the perpendicular OH to the chord AB.
OH is the height and median of triangle AOB, then AH = BH = AB / 2 = 8/2 = 4 cm, and triangles AOH and BOH are rectangular.
By the Pythagorean theorem, OH ^ 2 = AO ^ 2 – AH ^ 2 = 25 – 16 = 9.
OH = 3 cm.
Answer: From point O to chord AB 3 cm.
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