Circle Properties and Theorems Worksheets Grade 10

1. A circle has a radius of 15 cm. Two tangents are drawn from an external point P to the circle. The distance from P to the center of the circle is 17 cm. Find the length of each tangent segment.
2. 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?
3. A circular fountain with a radius of 10 meters is being designed for a city park. The landscape architect wants to create a triangular seating area inside the fountain where the vertices of the triangle lie on the circumference. If the triangle is equilateral, what is the exact area of this triangular seating area in square meters?

1. Liam is designing a circular garden with a central fountain. The garden has a radius of 15 meters, and he wants to install a decorative stone path that forms a chord 24 meters long. What is the perpendicular distance from the center of the fountain to this chord?
2. In a circle with center O, a chord AB is drawn. The perpendicular from O to AB meets AB at point M. If OM = 7 and the radius of the circle is 25, find the length of chord AB.
3. A city is designing a circular park with a central fountain. The park has a radius of 25 meters. A straight walking path connects two points on the circular edge, and this path is located 7 meters from the center of the park at its closest point. What is the length of this walking path in meters?

…and 2 more problems

1. Mason draws a circle with center O and radius 17 cm. Two chords AB and CD intersect at point E inside the circle. Chord AB is divided into segments AE = 7 cm and EB = 22 cm. Chord CD is divided into segments CE = 12 cm and ED = x cm. What is the value of x?
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. In a circle with center O, two chords AB and CD intersect at point E inside the circle. If AE = 9, EB = 16, CE = 8, find ED.

…and 2 more problems