Question

Хорды АВ и CD пересекаются в точке F так,что AF=4см,BF=16см,CF=DF.Найдите пожайлуста CD.

Answer 1

Если хорды окружности пересекаются, то произведение отрезков одной хорды равно произведению отрезков другой хорды, значит имеем:

AF*FB=CF*FD, По условию CF=FD, обозначим CF-через Х, получим:

х*х=4*16,

х(в квадр)=64,

х=8

х= -8-не является решением задачи, значит CF=FD=8см, следовательно CD=16см.

Answer 2

Given Information

We are given that the chords AB and CD intersect at point F, such that AF = 4 cm, BF = 16 cm, and CF = DF.

Solution

To find the length of CD, we can use the property of intersecting chords. 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 to find the length of CD. Let's denote the length of CF as x. Since CF = DF, the length of DF is also x.

Using the property of intersecting chords, we have:

AF * BF = CF * DF

Substituting the given values, we get:

4 cm * 16 cm = x * x

64 cm^2 = x^2

Taking the square root of both sides, we find:

x = 8 cm

Therefore, the length of CD is 8 cm.

Answer: CD = 8 cm