Question

Из точки М проведены секущие окружности МАВ и МСД.Найдите СД,если МВ=10,МД=15,СД=МА

Answer 1

Произведения отрезков секущих, проведенных из одной точки, равны:
МС*МД=МА*МВ
(МД-СД)*МД=СД*МВ
(15-СД)*15=10СД
225=25СД
СД=9

Answer 2

Problem Statement

We are given that point M is the center of two intersecting circles, circle MAV and circle MSD. We need to find the length of SD if MV = 10, MD = 15, and SD = MA.

Solution

To find the length of SD, we can use the properties of intersecting circles. Let's break down the problem step by step.

1. We are given that MV = 10 and MD = 15. Since M is the center of circle MAV, we can conclude that MA = MV + VA. Similarly, since M is the center of circle MSD, we can conclude that MS = MD + SD.

2. We are also given that SD = MA. Therefore, we can write the equation SD = MV + VA.

3. Combining the equations from steps 1 and 2, we have SD = MV + VA = MD + SD.

4. Rearranging the equation, we get SD - SD = MD - MV.

5. Simplifying the equation, we have 0 = MD - MV.

6. Since MD = 15 and MV = 10, we can substitute these values into the equation to find SD.

Therefore, SD = 15 - 10 = 5.

The length of SD is 5 units.

Please let me know if you need any further clarification.