Special Segments in a Circle Find measures of
- Slides: 14
Special Segments in a Circle • Find measures of segments that intersect in the interior of a circle. • Find measures of segments that intersect in the exterior of a circle. A Tibetan Mandala exhibiting a six-pointed star.
SEGMENTS INTERSECTING INSIDE A CIRCLE 1) Construct two intersecting chords in a circle. 2) Name the chords PQ and RS intersecting at T. 3) Draw PS and RQ. R P T S Q
SEGMENTS INTERSECTING INSIDE A CIRCLE R P Analyze: PTS RTQ Vertical Angles T S P R Angles intercept the same arc By angle-angle similarity, or PT ∙ TQ = RT ∙ ST Q
Theorem If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal. R P T S or PT ∙ TQ = RT ∙ ST Q
Example 1 Intersection of Two Chords D Find x A C 4 x 3 E 6 B
Example 2 Intersection of Two Chords Find x x 12 9 8
Example 3 What is the radius of the circle containing the arc if the arc is not a semicircle? Solve Problems 12 24 24
Example 3 continued What is the radius of the circle containing the arc if the arc is not a semicircle? Solution: 24 x 24 = 12 x 576 = 12 x 48 = x Diameter = 48 + 12 = 60 Radius = 60/2 = 30 Solve Problems 12 24 24 x
SEGMENTS INTERSECTING OUTSIDE A CIRCLE Theorem B C A E D If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
Example 4 Intersection of Two Secants Find RS if PQ = 12, QR = 2, and TS = 3. Let RS = x P 12 2 Q 3 R x S T Disregard the negative value
Example 5 Intersection of Two Secants Find x if EF = 10, EH = 8, and FG = 24. E 10 8 F x H 24 G I
Theorem X W Z Y If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Example 6 Intersection of a Secant and a Tangent Find x. A 4 B x+2 C x D The expression is not factorable. Use the quadratic formula. or Disregard the negative solution
Example 7 Find x. Intersection of a Secant and a Tangent x+2 x x+4 Disregard the negative value
- Special segments in circles
- 10-7 practice special segments in a circle
- Line segment example
- Congruent segment definition geometry
- Special segments in triangles worksheet
- Special segments test review
- Special segments in triangles
- 1-1 lesson quiz measuring segments and angles
- Repeated-measures design
- Find m
- Find the following arc measures
- 110/2
- Adjacent angles in parallel lines
- Kite and trapezoid
- Find the measures of the numbered angles in rhombus defg