1. A chord is drawn in a circle with a radius of 5 cm, at a distance of 3 cm from the center. What will be the length of that chord?

(a) 8 cm (b) 2 cm (c) 5 cm (d) 3 cm

2. Niyamat has drawn a circle with a radius of 13 cm. I have drawn a chord AB of length 10 cm in this circle. Calculate and write the distance from the center of the circle to this chord AB.

3. The radius of a circle is 13 cm and the length of a chord is 10 cm. What is the distance from the center of the circle to the chord?

(a) 12.5 cm (b) 12 cm (c) \(\sqrt{69}\) cm (d) \(\sqrt{24}\) cm

4. A circle has center O and a radius of 5 cm. AB is a chord of the circle with a length of 8 cm. Calculate and write the distance from point O to the chord AB.

5. A circle is centered at point O with a radius of 10 cm. A perpendicular is drawn from O to a chord AB, and the length of this perpendicular is 6 cm. What is the length of the chord AB?

6. The radius of a circle with center \(O\) is 5 cm. Point \(P\) is located at a distance of 13 cm from \(O\). From point \(P\), two tangents \(PQ\) and \(PR\) are drawn to the circle. Find the area of the quadrilateral \(PQOR\).

(a) \(60\) square cm (b) \(30\) square cm (c) \(120\) square cm (d) \(150\) square cm

7. A circle with center O has a radius of 10 cm. PQ is a chord with a length of 16 cm. The length of the perpendicular drawn from O to PQ is —

(a) 8 cm (b) 10 cm (c) 16 cm (d) 6 cm

8. From point A, which is located 26 cm away from the center O of a circle, a tangent is drawn to the circle with a length of 10 cm. Find the radius of the circle.

9. 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?

10. The radius of a circle is 13 cm. If the length of a chord AB in that circle is 10 cm, find the perpendicular distance from the center of the circle to the chord.

11. If a chord of a circle with radius 5 cm has a length of 4 cm, then the distance of the chord from the center is \(\_\_\_\_\) cm.

12. Point P is an external point to a circle with center O. The distance from point P to the center of the circle is 26 cm, and the length of the tangent drawn from point P to the circle is 10 cm. The radius of the circle is ____ cm.

13. If the perpendicular distance from the center of a circle with a radius of 17 cm to a chord is 4 cm, what is the length of the chord?

14. If a circle has a radius of 5 cm and a tangent is drawn from an external point \(P\) to the circle with a length of 12 cm, what is the distance from the center to point \(P\)?

15. For a circle centered at \(O\) with a radius of 5 cm and a chord length of 4 cm, the perpendicular distance from \(O\) to the chord is –?

(a) 3 cm (b) 1 cm (c) 4 cm (d) 2 cm

16. If a circle is centered at point 'O' with a radius of 13 cm and chord AB has a length of 10 cm, what is the distance from point 'O' to chord AB?

17. The radius of a circle centered at point O is 5 cm, and AB is a chord of length 8 cm. Calculate and write the distance from point O to the chord AB.

18. I have drawn a circle with center O and radius 6 cm. From a point P located 10 cm away from the center O, a tangent PT is drawn to the circle. Calculate and write the length of the tangent PT.

19. The radius of a circle with center O is 5 cm. From an external point P, which is located at a certain distance from point O, two tangents PQ and PR are drawn to the circle. The quadrilateral PQOR has an area of 60 square centimeters. Find the distance from point O to point P.

20. A circle with a radius of 10 cm has two parallel chords of lengths 4 cm and 6 cm. What is the distance between the two chords?

(a) \(\sqrt7(\sqrt3-\sqrt{12})\) cm (b) \(\sqrt3(\sqrt7+\sqrt{12})\) cm (c) \(\sqrt{13}(\sqrt{12}-\sqrt{7})\) cm (d) \(\sqrt{7}(\sqrt{13}+\sqrt{12})\) cm

21. 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.

22. Two parallel chords of a circle with a radius of 5 cm have lengths of 6 cm and 8 cm. What is the distance between the two chords?

23. AB is a chord (not a diameter) of a circle with center O. If the length of chord AB is 8 cm and the radius of the circle is 5 cm, find the perpendicular distance from the center O to the chord AB.

24. A circle is centered at O with a radius of 6 cm. From a point P located 10 cm away from the center O, determine the length of the tangent PT, where T is the point of tangency.

25. The diameter of a circle centered at O is 26 cm. The perpendicular distance from point O to the chord PQ is 5 cm. Determine the length of the chord PQ.

26. The radius of a circle is 13 cm, and the length of a chord in the circle is 10 cm. Determine the perpendicular distance from the center to the chord.

(a) 12 cm (b) \(\sqrt{69}\) cm (c) 24 cm (d) 12.5 cm

27. If the perpendicular drawn from the center of a circle with a radius of 10 cm to a chord is 6 cm long, then the length of the chord is ______.

28. Two equal circles, each with a radius of 10 cm, intersect, and the length of their common chord is 12 cm. Determine the distance between the centers of the circles.

29. Two identical circles, each with a radius of 10 cm, intersect, and the length of their common chord is 12 cm. Determine the distance between the centers of the two circles.

30. The diameter of a circle centered at O is 26 cm. The distance from point O to the chord PQ is 5 cm. Calculate and write the length of the chord PQ.