Through point A lying on the circle, the diameter AB and the chord AC are drawn, and AC = 8
| April 9, 2021 | education
Through point A lying on the circle, the diameter AB and the chord AC are drawn, and AC = 8 BAC = 30 Find the path CM, perpendicular to AB?
In the ABC triangle, the ACB angle is based on the AB diameter, therefore its value is 90, and the ABC triangle is rectangular.
By condition, CM is perpendicular to AB, then the segment CH is the height CH of the triangle ABC. In a right-angled triangle ACН, the CH leg lies opposite an angle of 30, and therefore is equal to half the length of the AC hypotenuse.
CH = AC / 2 = 8/2 = 4 cm.
The diameter of the circle AB divides the chord CM in half, since they are perpendicular, then the length of the chord CM = 2 * CH = 2 * 4 = 8 cm.
Answer: The length of the CM chord is 8 cm.
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