Theorems
"When two chords intersect inside a circle, the product of the segments of one chord equals ____________."
the product of the segments of the other chord.
What was the lesson about?
Circles and Lengths of Segments
What is a tangent segment?
A segment that starts outside at the circumference and ends outside the circle.
Two chords intersect inside a circle, AB and CD, intersecting at P. If AP=x, PB=3, CP=4, and PD=6, find x.
x=8
What is a circle?
The set of points in a plane at a given distance from a given point in that plane.
"When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals ________________."
the product of the other secant segment and its external segment.
What was theorem 9-11 about?
Segments of a chord.
What are segments of a chord?
Segments that start inside at the circumference and end inside where it is cut by another chord.
Secant AP and CP are drawn from a circle, meeting at external point P. AP intersects the circle at point B, and CP intersects at D. If AP=8, BP=x, CP=12, and DP=4, find x.
x=6
What is the center of a circle?
A given point from which a set of points in a plane are at given distance from.
"When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to _______________."
the square of the tangent segment.
What was theorem 9-12 about?
Secant segments.
What are secant segments?
Segments that start inside at the circumference and end outside the circle.
Secant AB and tangent AC are drawn from a circle, meeting at external point A. AB intersects the circle at point P. If AC=10, AP=x, and PB=3x, find x.
x=5
What is the radius?
The given distance from which a set of points in a plane are from a given point in that plane.
Two chords intersect inside a circle, AB and CD, intersecting at P. If CP=8, PD=6, AP=x, PB=3x, find the value of x.
x=4
What was theorem 9-13 about?
Tangent segments.
What are external secant segments?
The outside portions of a secant segment.
Secant AP and CP are drawn from a circle, meeting at external point P. AP intersects the circle at point B, and CP intersects at D. If AB=x, BP=4, CD=3, and DP=5, find x.
x=6
What are concentric circles?
Circles that lie in the same plane and have the same center.
Two secant segments are drawn to a circle from an external point at P, PA and PC. PA=9 and PC=x+3. If the external segment of PA is 4 and the external segment of PC is 3, find x.
x=9
What expression did the yellow circle guy have on the very first slide?
A laughing to tears expression.
Two chords intersect inside a circle, AB and CD, intersecting at P. What would segments AP and PB be called?
The segments of chord AB.
Secant AB and tangent AC are drawn from a circle, meeting at external point A. AB intersects the circle at point P. If AC=x, AP=3, and PB=4, find x.
x=square root of 21
What is the central angle of a circle?
An angle with its vertex at the center of the circle.