Presentation on theme: "1. 5. 4. 3. 2.. Tangents Sec: 12.1 Sol: G.11a,b A line is ______________________ to a circle if it intersects the circle in exactly one point. This point."— Presentation transcript:
Tangents Sec: 12.1 Sol: G.11a,b
A line is ______________________ to a circle if it intersects the circle in exactly one point. This point is called the point of _______________________________.
Consider the following diagram:
Example: If RT is tangent to Circle O, Then OR RT
The converse of the last theorem is also true. This means: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle. If OR RT, RT is tangent to Circle O
If a line is tangent to a circle, then it is ________________________________ to the radius drawn to the point of tangency. Example:
Theorem 10.11: If two __________from the same exterior point are tangent to a circle, then the two segments are ______. Example: AB CB
Example x+4 y 10 y-5
Circumscribed polygons: A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle. ◦ Example:
Example: Triangle HJK is circumscribed about circle G. Find the Perimeter of HJK if NK = JL JL + 29
Arcs and Chords Sec: 12.2 Sol: G.11a,b
Recall the definitions of minor arcs & chords (draw an example of each on A below): Example: When minor arc and a chord share the same endpoints, we call the arc the arc of the chord. Example:
In a circle or in congruent circles, two __________ ________ are congruent if and only if their corresponding chords are congruent. Example: In A, if, then ____ ____.
In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc. Example:
In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Example:
Find x in each problem Suppose a chord of a circle is 10 inches long and is 12 inches from the center of the circle. Find the length of the diameter. 3. Suppose the diameter of a circle is 34 inches long and a chord is 30 inches long. Find the distance between the chord and the center of the circle. 4. Suppose a chord of a circle is 24 cm long and is 15 cm from the center of the circle. Find the length of the radius.