Question

Хорды аб и сд пересекаются в точке е. найдите длину аб, если се=8 см, де-9см, а длина ае в 2 раза больше длины бе

Answer 1

8*9=2x*x

72=2x^2

x^2=36

x=6

Ответ  

6 +12=18см

Answer 2

Solving for the Length of AB

To find the length of AB, we can use the intersecting chords theorem, which states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

Given: - SE = 8 cm - DE = 9 cm - AE is twice the length of BE

Let's denote: - AE as x - BE as y

According to the intersecting chords theorem: - AE * CE = BE * DE

Applying the Intersecting Chords Theorem

Using the given information, we can set up the equation: - x * (x + 8) = y * (y + 9)

Solving for the Length of AB

We also know that AE is twice the length of BE: - x = 2y

Substituting x = 2y into the equation: - 2y * (2y + 8) = y * (y + 9)

Solving this equation will give us the value of y, which represents the length of BE. Once we have the value of y, we can find the length of AB, which is the sum of AE and BE.

Let's solve the equation to find the value of y and then calculate the length of AB.