Let's learn how to calculate the geometric mean. This is a concept video useful for Mathematics Olympiad and ISI and CMI Entrance.
Suppose a and b are positive numbers then their geometric mean is defined as square root of a times b. This is the formula of geometric mean.
We will construct the geometric mean of a and b geometrically. So, here are the steps:
7. Now, join XN and YN, and then look at the triangles YMN and XMN and try to show that these two triangles are actually similar. Now, see the following proof:
8. Since, we know that similar triangles have proportional sides. So, we can say,
Hence, this is proved.
Hope you liked it!