1. 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?

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. A chord is drawn at a distance of 5 cm from the center of a circle with a radius of 10 cm. What is the length of the chord?

(a) \(5\sqrt3\) cm (b) 6 cm (c) 8 cm (d) 3 cm

4. 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.

5. 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.

6. 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.

7. 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 ______.

8. 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.

9. 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.

10. 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.

11. 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

12. 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?

13. 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

14. 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

15. 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.

16. 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?

17. 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.

18. 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?

19. 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.

20. 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 \(P\)?

21. The length of a chord of a circle is 14 cm, and the perpendicular distance from the center to the chord is 24 cm. Find the radius of the circle.

22. 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

23. 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.

24. 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.

25. The radius of a circle is 13 cm and the length of a chord is 10 cm. Find the distance from the center of the circle to the chord.

(a) 12.5 cm (b) 12 cm (c) √69 cm (d) 24 cm

26. 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.

27. Write the length of the chord of a circle with a radius of 17 cm, if its distance from the center is 4 cm.

28. Let's draw a circle with a radius of 2.5 cm. Take a point outside the circle that is 6.5 cm away from the center. Then, draw a tangent to the circle from that external point and measure the length of the tangent using a ruler.

29. 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.

30. 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