A chord equal to 30 cm is drawn in a circle R = 17 cm. Find the distance from the center of the circle to the chord.
| February 26, 2021 | education
The distance from the center of the circle to the chord AB will be the perpendicular OH, which will be the height of the triangle AOB.
The AOB triangle is isosceles, since ОА = ОВ = R = 17 cm.Then the height ОН will also be the median of the ВОА triangle, and then AH = ВН = AB / 2 = 30/2 = 15 cm.
In the right-angled triangle AON, we determine the length of the leg OH using the Pythagorean theorem.
OH ^ 2 = OA ^ 2 – BH ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64.
OH = 8 cm.
Answer: The distance from point O to the BC chord is 8 cm.
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