1. If two circles touch each other externally, the number of common tangents will be 3.
2. If two circles do not touch or intersect each other, the number of common tangents between them is—
(a) 2 (b) 1 (c) 3 (d) 4
3. If two circles do not touch or intersect each other, the number of common tangents between them is—?
4. If two circles do not touch or intersect each other, the number of common tangents between them is
(a) 2 (b) 3 (c) 4 (d) 1
5. If two circles neither intersect nor touch each other, the maximum number of common tangents that can be drawn to them is _________.
6. If two circles touch each other externally at point A, and the number of direct common tangents is \(= x\), and the number of transverse common tangents is \(= y\), then \(x - y =-----\).
7. If two circles do not touch or intersect each other, there can be a maximum of ______ common tangents.
8. The radii of two circles are 3.5 cm and 2 cm. The circles touch each other internally. The distance between the centers of the two circles will be –
(a) 5.5 cm (b) 1 cm (c) 1.5 cm (d) None of the above
9. If two circles do not intersect or touch each other, then a maximum of _____ common tangents can be drawn between them.
10. If two circles neither intersect nor touch each other, a maximum of 4 common tangents can be drawn.
11. The radii of two circles are 5 cm and 3 cm, respectively. If the circles touch each other externally, then the distance between their centers will be –
(a) 2 cm (b) 3 cm (c) 8 cm (d) 1.5 cm
12. If two circles are externally tangent to each other, the maximum number of common tangents is _____.
13. Two circles touch each other externally at point \(C\). \(AB\) is a common tangent to the two circles, touching them at points \(A\) and \(B\), respectively. The measurement of \(\angle ACB\) is –
(a) 60° (b) 45° (c) 30° (d) 90°
14. If two circles with diameters of 5 cm and 7 cm touch each other internally, then the distance between their centers is —
(a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm
15. Two circles touch each other externally at point C. AB is a common tangent to both circles and touches the circles at points A and B, respectively. Find the measure of \(\angle\)ACB.
16. The radii of two circles are 5 cm and 3 cm. If the two circles are externally tangent to each other, the distance between their centers will be -
(a) 2 cm (b) 2.5 cm (c) 1.5 cm (d) 8 cm
17. The radii of two circles are 5.5 cm and 2 cm. The circles touch each other internally. The distance between the centers of the two circles is —
(a) 3.5 cm (b) 2.5 cm (c) 1.5 cm (d) 7.5 cm
18. Two circles touch each other externally. The distance between their centers is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle is —
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm
19. If two circles with radii \(r_1\) and \(r_2\) touch each other externally, and the distance between their centers is \(d\), then which of the following is correct?
(a) \(r_1+d=r_2\) (b) \(r_2+d=r_1\) (c) \(r_1+r_2=d\) (d) \(r_1-r_2=d\)
20. Two identical circles, each with radius \(r\), intersect in such a way that each circle passes through the center of the other. The centers of the circles are labeled A and B, and they intersect at points P and Q. The area of triangle \(\triangle APB\) will be:
(a) \(\cfrac{\sqrt3}{4}r^2\) (b) \(\cfrac{\sqrt3}{2}r^2\) (c) \(\cfrac{\sqrt3}{3}r^2\) (d) \(\sqrt3 r^2\)
21. Two circles touch each other externally. The diameters of the circles are 7 cm and 6 cm respectively. What is the distance between their centers?
(a) 6 cm (b) 13 cm (c) 12.5 cm (d) 6.5 cm
22. Two circles intersect each other. The radius of each circle is 10 cm. The length of the common chord is 16 cm. Find the distance between the centers of the two circles.
23. Two identical circles, each with a radius of 10 cm, intersect each other, and the length of their common chord is 12 cm. Find the distance between the centers of the two circles.
24. If two circles touch each other internally, they have only one common straight tangent.
25. If two circles touch each other internally, they have only one common straight tangent.
26. Two identical circles, each with a radius of 13 cm, intersect each other, and the length of their common chord is 10 cm. What is the distance between the centers of the two circles?
27. If two circles with radii of 10 cm and 7 cm are internally tangent to each other, the distance between their centers will be—
(a) 4 cm (b) 6 cm (c) 17 cm (d) 3 cm
28. Two circles touch each other externally at point \( C \). A common external tangent touches the two circles at points \( A \) and \( B \). Determine the value of \( \angle ACB \).
29. Two circles touch each other externally at point C. A common tangent AB touches the circles at points A and B respectively. Find the value of \(\angle ACB\).
30. Two equal circles, each with a radius of 10 cm, intersect each other. The length of their common chord is 12 cm. Find the distance between their centers.
