1. Draw a circle with a radius of 4 cm. From a point located 6.5 cm away from the center of the circle, draw two tangents to the circle.
2. 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.
3. 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.
4. 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
5. The radius of a circle centered at point O is 5 cm. Point P is located 13 cm away from point O. PQ and PR are two tangents drawn from point P to the circle. What is the area of quadrilateral PQOR?
6. Let’s draw a circle with a radius of 2.8 cm. Then, take a point that is 7.5 cm away from the center of the circle. From that external point, draw two tangents to the circle.
7. 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.
8. What is the length of the tangent drawn from an external point located 17 cm away from the center of a circle with a radius of 4 cm?
9. Find the length of the tangent drawn from a point located 13 cm away from the center of a circle with a radius of 5 cm.
10. Draw a circle with a radius of 2.6 cm and, from a point 6 cm away from the center (outside the circle), draw a tangent to the circle.
11. If I draw a circle centered at point O, and from a point P located 26 cm away from the center a tangent is drawn to the circle which measures 10 cm in length, then calculate and write the length of the radius of the circle.
12. 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.
13. From a point outside a circle, a tangent of length 8 cm is drawn to the circle. If the radius of the circle is 6 cm, what is the distance from the center of the circle to the external point?
(a) 10 cm (b) 8 cm (c) 6 cm (d) 14 cm
14. From an external point located 17 cm away from the center of a circle with a diameter of 16 cm, what is the length of the tangent drawn to the circle?
15. 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.
16. 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.
17. Find the length of the tangent drawn from an external point located 17 cm away from the center of a circle with a diameter of 16 cm.
18. What is the length of the tangent drawn from an external point located 17 cm away from the center of a circle with a radius of 16 cm?
19. Draw a straight line segment AB of radius 3 cm. With point A as the center and radius equal to AB, draw a circle. Then, draw a tangent to the circle at point B.
20. Point P lies on a circle with center O. At point P, draw a tangent to the circle, and from that tangent, mark a segment PQ equal in length to the radius of the circle. From point Q, draw another tangent QR to the circle. Using a protractor, measure the angle ∠PQR and write down its value.
21. The radius of a circle centered at point O is 5 cm. Point P lies at a distance of 13 cm from point O. From point P, two tangents PQ and PR are drawn to the circle. Find the area of quadrilateral PQOR.
(a) 60 square cm (b) 30 square cm (c) 120 square cm (d) 150 square cm
22. In a circle with center O, a tangent PT is drawn from an external point P to the circle, with T being the point of tangency. If PT = 12 cm and OP = 13 cm, the diameter of the circle will be:
(a) 5 cm (b) 8 cm (c) 6 cm (d) 10 cm
23. 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?
24. 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 \(P\)?
25. A circle has center ‘O’, and a point P lies 26 cm away from it. If the length of the tangent drawn from point P to the circle is 10 cm, then what is the radius of the circle?
26. 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.
27. Draw a straight line segment XY with a length of 4 cm, and use XY as the diameter to draw a circle. At points X and Y, draw tangents to the circle, and write about the relationship between these two tangents.
28. Draw an equilateral triangle ABC with each side measuring 5 cm. Then, draw the circumcircle of that triangle. At point A on the circle, draw a tangent. On the tangent, take a point P such that AP = 5 cm. From point P, draw another tangent to the circle, and write down which point on the circle this second tangent touches.
29. Write the length of the tangent drawn from an external point located 17 cm away from the center of a circle that has a diameter of 16 cm.
30. The distance from the center of a circle to an external point is 13 cm. The length of the tangent from that point to the circle is 12 cm. The radius of the circle is—
(a) 25 cm (b) 1 cm (c) 5 cm (d) \(\cfrac{13}{12}\) cm
