In the rectangle МРКН О – the point of intersection of the diagonals. Points A and B are the midpoints

| March 15, 2021 | education

In the rectangle МРКН О – the point of intersection of the diagonals. Points A and B are the midpoints of the sides МР and МН, respectively. Point C divides the segment MK in a ratio of 1: 7, counting from point M. AC is perpendicular to MK. Find the ratio BO: RN.

Let the length of the segment MS = X cm, then, by condition, KС = 7 * X cm.

The length of the diagonal MK = MС + KС = X + 7 * X = 8 * X cm.

Then MO = MK / 2 = 4 * X.

CO = MO – MС = 3 * X.

Since MРKN is a rectangle, then PH = MK = 8 * X cm.

Let’s connect points A and O. Since point A is the middle of MP, and point O is the middle of PH, then AO is the middle line of triangle MPH, which means AO is parallel to MP and perpendicular to MP.

Then AC is the height drawn to the MO hypotenuse.

AC ^ 2 = MC * OC = X * 3 * X = 3 * X2.

From the right-angled triangle AMC, according to the Pythagorean theorem, we define AM.

AM ^ 2 = AC ^ 2 + MC ^ 2 = 3 * X ^ 2 + X ^ 2 = 4 * X ^ 2.

AM = 2 * X, then OB = 2 * X.

OB / РН = 2 * X / 8 * X = 1/4.

Answer: 1/4.



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.