Question

Хорды АВ и СD пересекаются в точке K. АК=6 см., ВК=8 см.,СК=4 см. Найдите длину DK?

Answer 1

треугольники акс и треугольник квд являются подобными по 1 углу и 2-ум сторонам

коэфицент подобия к=2

кд=6х2=12

Answer 2

Problem Analysis

We are given that chords AB and CD intersect at point K. We are also given the lengths AK, BK, and CK. We need to find the length of DK.

Solution

To find the length of DK, 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.

In this case, we can use the property as follows:

AK * BK = CK * DK

Substituting the given values, we have:

6 * 8 = 4 * DK

Simplifying the equation, we get:

48 = 4 * DK

Dividing both sides by 4, we find:

DK = 48 / 4 = 12 cm

Therefore, the length of DK is 12 cm.

Conclusion

The length of DK is 12 cm.