Question

хорды АВ и СВ круга пересекаются в точке М, которая делит хорду АВ на отрезки 2 см и 4 см. На какие отрезки делит точка М хорду СD, если один из них больше в два раза чем другой

Answer 1

Действую по свойству хорд:

2*4=2х*х

4=х*х

х=2

Значит отвезок СД разбит точкой М на отрезки 2 см и 2*2=4см

Ответ: 2см, 4 см.

Answer 2

Intersection of Chords AB and CD

The chords AB and CD intersect at point M, which divides chord AB into segments of 2 cm and 4 cm. We need to determine how point M divides chord CD into two segments, with one segment being twice the length of the other.

To solve this problem, we can use the property of intersecting chords in a circle. According to this property, when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Let's denote the lengths of the segments of chord CD as x and 2x (where 2x is twice the length of x). We know that the lengths of the segments of chord AB are 2 cm and 4 cm. Therefore, we can set up the following equation:

2 cm * 4 cm = x * 2x

Simplifying the equation:

8 cm^2 = 2x^2

Dividing both sides by 2:

4 cm^2 = x^2

Taking the square root of both sides:

2 cm = x

Therefore, one segment of chord CD is 2 cm and the other segment is 4 cm, with one segment being twice the length of the other.

Answer: Point M divides chord CD into segments of 2 cm and 4 cm, with one segment being twice the length of the other.