Question

Окружность,AC и BD-хорды,пересекаются в точке m. MC<AM на 3,5. DM=4 и BM=0.5.Найти AC

Answer 1

Точка М-пересечение, МС=х, АМ=МС+3,5=х+3,5, АМ*МС=ВМ*ДМ, х*(х+3,5)=0,5*4, х в квадрате+3,5х=2, х в квадрате+3,5х-2=0, х=1/2*(-3,5)+-корень(12,25+4*2), х1=0,5, второе значение отрицательное, МС=0,5, АМ=0,5+3,5=4, АС=4+0,5=4,5

Answer 2

Problem Analysis

We are given a circle with chords AC and BD intersecting at point M. We are also given that MC is 3.5, DM is 4, and BM is 0.5. We need to find the length of AC.

Solution

To find the length of AC, we can use the intersecting chords theorem, which states that 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 length of AM as x and the length of CM as y. Since MC is 3.5, we have y = 3.5. We are also given that DM is 4 and BM is 0.5.

According to the intersecting chords theorem, we can write the following equation:

AM * BM = CM * DM

Substituting the given values, we have:

x * 0.5 = 3.5 * 4

Simplifying the equation, we get:

0.5x = 14

Dividing both sides by 0.5, we find:

x = 28

Therefore, the length of AM is 28.

To find the length of AC, we can use the Pythagorean theorem. In a right triangle with sides AM, CM, and AC, we have:

AC^2 = AM^2 + CM^2

Substituting the values, we have:

AC^2 = 28^2 + 3.5^2

Calculating the values, we find:

AC^2 = 784 + 12.25

AC^2 = 796.25

Taking the square root of both sides, we find:

AC ≈ 28.23

Therefore, the length of AC is approximately 28.23.

Answer

The length of AC is approximately 28.23.