In a circle with center O and radius OA. The distance from the center O to the chord BC is 3 cm.
| September 20, 2021 | education
In a circle with center O and radius OA. The distance from the center O to the chord BC is 3 cm. Find the length of the chord if the angle OBC = 45 degrees.
From the center of the circle, point O, we construct a perpendicular OH = 3 cm.
By condition, the angle ОВС = 450, then the right-angled triangle ОВН is isosceles, ВН = ОН = 3 cm.
In right-angled triangles BOH and COH, the leg OH is common, OB = OC = R, then the triangles are equal in leg and hypotenuse. Then CH = BH = 3 cm.
ВС = ВН + СН = 3 + 3 = 6 cm.
Answer: The length of the BC chord is 6 cm.
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