Circles O and P are internally tangent?

Question

The radius of cicle O is 12 cm and the radius of circle P is 8 cm. Find the distance OP (the line of centers).

Answer 1

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we've got ourselves 2 circles... one inside of the other and they touch at 1 point...

O is the center point of the circle with radius 12

and p is the center point of the circle with radius 8...

so... if you look at the far left point of both of these circles (assuming this is the point they share)... it's gotta be 12 cm from O and 8 cm from p alon the same line, so

OP = 12-8=4

Answer 2

The center of circle O is 12 cm from the point of tangency. The center of circle P is 8 cm from the point of tangency. The center of P is between the center of O and the point of tangency since the circles are internally tangent. Thus the distance between their centers is 12 cm - 8 cm = 4 cm.