c hapter 11 c ircles. s ection 11 – 1 t angent l ines objectives: to use the relationship between...
TRANSCRIPT
SECTION 11 – 1 TANGENT LINES
Objectives:• To use the relationship
between a radius and a tangent
• To use the relationship between two tangents from one point
A TANGENT TO A CIRCLE:
A line, ray or segment in the plane of a circle that intersects the circle in exactly one point.
POINT OF TANGENCY:The point where a circle and a tangent intersect
A Tangent
Point of Tangency
THEOREM 11 – 1If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
EXAMPLE 2 REAL-WORLD CONNECTION
A) A dirt bike chain fits tightly around two gears. The chain and gears form a figure
like the one at the right. Find the distance between the centers of the gears.
EXAMPLE 2 REAL-WORLD CONNECTION
B) A belt fits tightly around two circular pulleys, as shown at the right. Find the distance between the centers of the pulleys.
EXAMPLE 2 REAL-WORLD CONNECTION
C) A belt fits tightly around two circular pulleys, as shown at the right. Find the distance between the centers of the pulleys.
THEOREM 11 – 2 (CONVERSE OF 11 – 1)
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.
EXAMPLE 3 FINDING A TANGENT
C) O has radius 5. Point P is outside O such that PO = 12, and Point A is on O such that PA = 13. Is tangent to O at A? Explain.
EXAMPLE 5 CIRCLES INSCRIBED IN POLYGONS
B) O is inscribed in ∆ PQR. ∆PQR has a perimeter of 88 cm. Find QY.
EXAMPLE 5 CIRCLES INSCRIBED IN POLYGONS
C) C is inscribed in quadrilateral XYZW. Find the perimeter of XYZW.
ADDITIONAL EXAMPLESAssume the lines that appear to be tangent are tangent. O is the center of each circle. Find the value of x.