Circle Properties and Theorems Worksheets Grade 10

1. In a circle with center O, radius 17 cm, chord AB is drawn. The perpendicular distance from O to AB is 8 cm. Find the length of chord AB.
2. A circle is defined by the equation x² + y² - 6x + 4y - 12 = 0. A line with equation y = 2x - 3 intersects the circle at two points. Find the exact length of the chord formed by this intersection.
3. A circle has center at (0,0) and radius 5. Find the length of the chord cut off by the line x = 3.

…and 2 more problems

1. Noah is designing a circular fountain for a botanical garden. The fountain has a radius of 34 meters. He wants to install a straight stone path that connects two points on the circumference. The perpendicular distance from the center of the fountain to this chord is 16 meters. At the midpoint of the chord, Noah plans to place a small bronze plaque, and from that plaque, he will run a straight water pipe to the center of the fountain. What is the total length of the water pipe in meters?
2. A circle with center (0,0) has radius 5. Find the length of the tangent from point (8,0) to the circle.
3. A circle with center (0,0) and radius 13 has a chord that is 24 units long. What is the perpendicular distance from the center of the circle to this chord?

…and 1 more problems

1. Hana is designing a circular fountain for a community plaza. The fountain has a radius of 13 meters. She wants to place two decorative lights at points A and B on the circumference such that the chord AB is exactly 24 meters long. From point A, she draws a tangent line to the circle. From point B, she draws another tangent line. These two tangent lines intersect at point C outside the circle. What is the exact length of AC, the distance from point A to the intersection point C of the tangents?
2. A circle with center (0,0) and radius 5 intersects the line y = 3 at two points. Find the distance between these intersection points.
3. Sophia is designing a circular fountain for a city plaza. The fountain has a radius of 12 meters. She wants to install a straight stone path that connects two points on the circumference, forming a chord. The perpendicular distance from the center of the fountain to this chord is 9 meters. At the midpoint of the chord, she plans to place a small statue, and from that statue, she will run a straight line to the center of the fountain. What is the length of the line from the statue to the center of the fountain in meters?