Question

Two circles with radii 25 cm and 9 cm touch each
other externally. Find the length of the direct
common tangent.​

Answer 1

Length of Direct common Tangent  = 30 cm

Step-by-step explanation:

Let say Direct Tangent PQ touching 25 cm radius Circle at P & 9 cm radius at Q

Let say length of PQ = 2a

Then a line RS  tangent at point touching circle ( R on PQ & S circle touching)

PR = RS   & QR = RS

=> PR = QR = RS = a

Now 25/a  = a/9

=> a² = 225

=> a = 15

2a = 30

Length of Direct common Tangent  = 30 cm

Learn more:

in the figure, points P B and Q are points of contacts of the respective ...

https://brainly.in/question/14976891

Answer 2

The length of the direct common tangent to circles with radii 25 cm and 9 cm touching externally is 30 cm.

    Given,

           $R_{1}=25cm$

           $R_{2}=9cm$

    Let the tangent touch the circles at points A and B respectively.

    Then length of the direct common tangent is given by

            $AB=2\sqrt{R_{1}R_{2}}$

            $AB=2\sqrt{(25)(9)}$

            AB = 2(5)(3)

            AB = 30 cm