The chord ab is 26 cm oa and ob is the radius of the circle and the angle aob is 120 degrees.

| January 6, 2021 | education

The chord ab is 26 cm oa and ob is the radius of the circle and the angle aob is 120 degrees. Find the distance from the point o to the chord ab.

From point O, the center of the circle, draw the radii OA and OB. Then the formed triangle AOB is isosceles, OA = OB. From point O we draw the height OH to the chord AB, which will also be the bisector and median of the triangle AOB.
Then AH = BH = AB / 2 = 26/2 = 13 cm.
Angle AON = AOB / 2 = 120/2 = 600.
In the right-angled triangle AOН, we determine the length of the OH leg.
The tangent of the angle of a right-angled triangle is equal to the ratio of the opposite leg to the adjacent one.
tgAOH = AO / OH.
OH = AН / tgAOH = 13 / √3 = 13 * √3 / 3 cm.
Answer: The distance from point O to the chord is 13 * √3 / 3 cm.



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