Lesson: Tangents of a Circle Mathematics

Students will be able to

• recall the definition of a tangent to a circle,
• understand that a tangent and a radius which share a common point on the circumference of a circle are perpendicular to each other,
• understand that the lengths of tangent segments drawn from an external point to a circle are equal in length and understand corollaries derived from this theorem such as
  • the bisector of the chord which connects to tangents,
  • the bisector of the central angle and the angle whose vertex is at the external point,
• understand the definition of the inscribed circle of a polygon
  • including how the center of the circle relates to the angle bisectors of the polygon,
• identify how to determine the center of the inscribed circle of a polygon,
• apply the properties of tangent of circles in order to find missing angles or side lengths, including systems
  • with circles inscribed in polygons,
  • with lines which are common tangents to more than one circle.