Two chords AB and CD are drawn in a circle centered at point O. Lines AB and CD are perpendicular

| August 17, 2021 | education

Two chords AB and CD are drawn in a circle centered at point O. Lines AB and CD are perpendicular and intersect at point M, which lies outside the arm. In this case AM = 36, BM = 6, CD = 4√46. Find OM.

Let us draw perpendiculars from point O to the chords AB and CD, which will divide these chords in half. ВK = AK = (AM – BM) / 2 = 30/2 = 15 cm.DН = СН = 4 * √46 / 2 = 2 * √46 cm.

Segment KM = BK + BM = 15 + 6 = 21 cm.

In a right-angled triangle ОНD, we define the length of the hypotenuse ОD equal to the radius of the circle.

OD ^ 2 = DН ^ 2 + KM ^ 2 = (2 * √46) ^ 2 + 15 ^ 2 = 184 + 441 = 625.

OD = OA = 25 cm.

From the right-angled triangle OAK, by the Pythagorean theorem, we determine the length of the leg OK.

OK ^ 2 = OA ^ 2 – AK ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

OK = 20 cm.

From the right-angled triangle OKM, by the Pythagorean theorem, we determine the length of the hypotenuse OM.

OM ^ 2 = OK ^ 2 + KM ^ 2 = 400 + 441 = 841.

OM = 29 cm.

Answer: The length of the segment OM is 29 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.