For two circles of radius 7 units and 7/2 units, whose centres are 15 units apart, what is the length of the direct common tangent in units? (Correct to 3 decimal places.)

Question

Accepted Answer

Given two circles with radii r1 = 7 units and r2 = 7/2 = 3.5 units, and the distance between their centers d = 15 units. We need to find the length of the direct common tangent.

The formula for the length (L) of the direct common tangent between two circles is:

L = sqrt(d^2 - (r1 - r2)^2)

Step 1: Calculate (r1 - r2):
7 - 3.5 = 3.5

Step 2: Square the distance between centers:
15^2 = 225

Step 3: Square the difference of radii:
3.5^2 = 12.25

Step 4: Substitute in formula:
L = sqrt(225 - 12.25) = sqrt(212.75)

Step 5: Calculate sqrt(212.75):
L ≈ 14.586 units

Therefore, the length of the direct common tangent is approximately 14.586 units.

Answer

Answer

Answer