Question

1) Хорды AB и CD пересекаются в точке F так, сто AF=4, BF=16, CF=32. Найти CD

Answer 1

По теореме о пересечении хорд в одной точке

АF * FB = CF * FD => 64 = 32 * FD

                              FD = 2

CD = CF + FD => 32 + 2 = 34. 

Answer 2

Given Information:

We are given that the chords AB and CD intersect at point F, and we are also given the lengths AF = 4, BF = 16, and CF = 32.

Solution:

To find the length of CD, 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. Mathematically, this can be expressed as:

AF * BF = CF * DF Substituting the given values, we have:

4 * 16 = 32 * DF

Simplifying the equation, we get:

64 = 32 * DF

Dividing both sides of the equation by 32, we find:

DF = 2

Therefore, the length of CD is 2.

Answer:

The length of CD is 2.