O-center of the circle, AB-diameter, CD-chord, AB perpendicular to CD OK = KD = 3cm
| September 27, 2021 | education
O-center of the circle, AB-diameter, CD-chord, AB perpendicular to CD OK = KD = 3cm Find: CD the degree measure of each angle.
Since, according to the condition, AB is perpendicular to CD, then the triangle DOK is rectangular, and since OK = KD, then it is isosceles, then the angle KOD = KDO = 45.
The radius perpendicular to the chord divides this chord in half, then CK = DK = 3 cm.
Then CD = CK + DK = 3 + 3 = 6 cm.
The KOS triangle is rectangular and isosceles, the angle KOС = OCK = 45.
Angle DОС = 45 + 45 = 90.
Answer: The length of the chord CD is 6 cm, the angles are 45, 90, 45.
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