New York State Common Core Math Geometry, Module 5, Lesson 11
Worksheets for Geometry, Module 5, Lesson 11
- Students discover that a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point.
- Students construct tangents to a circle through a given point.
- Students prove that tangent segments from the same point are equal in length.
Properties of Tangents
- 𝐶𝐷 and 𝐶𝐸 are tangent to circle 𝐴 at points 𝐷 and 𝐸, respectively. Use a two-column proof to prove 𝑎 = 𝑏.
- In circle 𝐴, the radius is 9 mm and 𝐵𝐶 = 12 mm.
a. Find 𝐴𝐶.
b. Find the area of △ 𝐴𝐶𝐷.
c. Find the perimeter of quadrilateral 𝐴𝐵𝐶𝐷.
- In circle 𝐴, 𝐸𝐹 = 12 and 𝐴𝐸 = 13. 𝐴𝐸: 𝐴𝐶 = 1: 3.
a. Find the radius of the circle.
b. Find 𝐵𝐶 (round to the nearest whole number).
c. Find 𝐸𝐶
- A tangent line to a circle is perpendicular to the radius of the circle drawn to the point of tangency.
- A line through a point on a circle is tangent at the point if, and only if, it is perpendicular to the radius
drawn to the point of tangency.
- INTERIOR OF A CIRCLE: The interior of a circle with center 𝑂 and radius 𝑟 is the set of all points in the plane
whose distance from the point 𝑂 is less than 𝑟.
A point in the interior of a circle is said to be inside the circle. A disk is the union of the circle with its
- EXTERIOR OF A CIRCLE: The exterior of a circle with center 𝑂 and radius 𝑟 is the set of all points in the plane
whose distance from the point 𝑂 is greater than 𝑟.
A point exterior to a circle is said to be outside the circle.
- TANGENT TO A CIRCLE: A tangent line to a circle is a line in the same plane that intersects the circle in one
and only one point. This point is called the point of tangency.
- TANGENT SEGMENT/RAY: A segment is a tangent segment to a circle if the line that contains it is tangent to
the circle and one of the end points of the segment is a point of tangency. A ray is called a tangent ray to
a circle if the line that contains it is tangent to the circle and the vertex of the ray is the point of tangency.
- SECANT TO A CIRCLE: A secant line to a circle is a line that intersects a circle in exactly two points.
- POLYGON INSCRIBED IN A CIRCLE: A polygon is inscribed in a circle if all of the vertices of the polygon lie on the
- CIRCLE INSCRIBED IN A POLYGON: A circle is inscribed in a polygon if each side of the polygon is tangent to the
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