Tangent Lines Skill 48 Objective HSGC 2 Students

Tangent Lines Skill 48

Objective HSG-C. 2: Students are responsible for using properties of tangents to circles.

Definitions A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point of where a circle and a tangent intersect is the point of tangency.

Theorem 79: Tangent Perpendicular to Radius If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency. P l O

Theorem 80: Radius Perpendicular to Tangent If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. P l O

Theorem 81: Congruent Tangents If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent. A B O C

Example 1; Finding Angle Measures L O xᵒ 117ᵒ N M

Example 1; Finding Angle Measures D O 38ᵒ xᵒ E

Example 2; Finding Distance a) The CN Tower in Toronto, Canada, has an observation deck 447 m above ground level. About how far is it from the observation deck to the horizon? Earth’s radius is about 6400 km. Convert meters to kilometers Recall the Pythagorean Theorem a c b

Example 2; Finding Distance b) What is the distance to the horizon that a person can see on a clear day from an airplane 2 mi above Earth? The Earth’s radius is about 4000 miles. Recall the Pythagorean Theorem a c b

Example 3; Finding a Radius b a 12 x A x c 8

Example 3; Finding a Radius b 10 a x B x c 6

Example 4; Identifying a Tangent M c 25 N a 24 b 7 L

Example 4; Identifying a Tangent M c 8 N a 7 4 L b

Example 5; Circles Inscribed in Polygons B 15 cm E C 8 cm O F D 10 cm A

Example 5; Circles Inscribed in Polygons Q X 15 cm O Y P Z 17 cm R

#48: Tangent Lines Ø Questions? Ø Summarize Notes Ø Homework Ø Quiz