Solve any five sub-questions:

If two circles with radii 8 and 3 respectively touch externally, then find the distance between their centers.

Let the circles with center A and B having radius 8 and 3 respectively touching externally at point M as shown

The line passing through the centers of both circle will pass through the point where both the circles touch

Distance between their centers is given by the distance AB

From diagram AB = AM + MB

AM = 8 because M is point on circle and A is center of circle therefore AM is the radius of big circle

MB = 3 because M is point on circle and B is center of circle therefore MB is the radius of small circle

∴ AB = 8 + 3

∴ AB = 11

Distance between centers is 11