TWO CIRCLES TOUCH INTERNALLY .THE SUM OF THEIR AREA IS 116phi sq. cm AND THE DISTANCE BETWEEN THEIR CENTRES IS 6 CM . FIND THE RADIIOF THE CIRCLES.
Let us observe the following figure.
Center of the bigger circle is O and the center of the smaller circle is A.
Distance between the centers of the circles, that is OA = 6cm.
Let x be the radius of the smaller circle and x + 6 cm be the radius of the bigger circle.
Area of the bigger circle is and the area of the smaller circle is .
Sum of the areas of the circle is .
Thus,
Neglecting the negative value, we have .
Thus, the radius of the smaller circle is 4cm and the radius of the bigger circle is 6 + 4 = 10 cm.
Thus, OA = 4 cm and OB = 10 cm