Question

Хорды MN и KL пересекаются в т.А,причем хорда MN делится т.А на отрезки равные 10см и 6см.На какие отрезки т.А делит хорду KL,если KL>MN на 3см.

Answer 1

Пусть МА равно 6 см, а АN равно 10см. Следовательно MN равно 16 см. KL равно 16+3=19см. Х см - KA. (19-X ) см - AL Используя формулу получаем MA*AN=KA*AL. 6*10=Х*(19-Х). 60=Х(19-Х). Х=4. Следовательно KA = 4см, а AL = 15см

Answer 2

Problem Analysis

We are given that chords MN and KL intersect at point A. Chord MN is divided into two segments at point A, with lengths of 10 cm and 6 cm. We need to determine how chord KL is divided at point A, given that KL is 3 cm longer than MN.

Solution

Let's assume that chord KL is divided into two segments at point A, with lengths x and y. Since KL is 3 cm longer than MN, we can express this relationship as:

KL = MN + 3

We also know that chord MN is divided into two segments at point A, with lengths of 10 cm and 6 cm. Therefore, we can write the following equation:

10 + 6 = x + y

Simplifying this equation, we get:

16 = x + y

Now, we have a system of two equations:

KL = MN + 3 16 = x + y

To solve this system, we can substitute the value of MN from the first equation into the second equation:

16 = (KL - 3) + y

Simplifying this equation, we get:

16 = KL - 3 + y

Rearranging the equation, we have:

y = 16 - KL + 3 y = 19 - KL

Therefore, chord KL is divided at point A into segments of 19 - KL and KL - 16.

Answer

Chord KL is divided at point A into segments of 19 - KL and KL - 16.