Question

The length of direct common tangents to two circles touching each other of radii 3 cm and 12 cm is 16 cm.
Calculate the distance between their centres.​

Answer 1

Answer:

√481

Step-by-step explanation:

The length of direct common tangents to two circles touching each other of radii 3 cm and 12 cm is 16 cm.

As we know,

The length of the transverse common tangent to the circle,

l = √(Distance)² - (R₁ + R₂)²

=> 16 = √(Distance)² - (3 + 12)²

=> 256 = (Distance)² - (15)²

=> 256 + 225 = Distance²

=> 481 = Distance²

=> Distance = √481.

Hope it helps!

Answer 2

Solution

$distance {}^{2} = (length \: of \: tangent) {}^{2} + (r1 + r2) {}^{2} \\ = > distance {}^{2} = 16 {}^{2} + (3 + 12) {}^{2} \\ = > distance = \sqrt{256 + 225} = \sqrt{481} \\ = > distance = 21.93$