Holt McDougal Geometry 12-6 Segment Relationships in Circles 9-6 Segment Relationships in Circles...
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Transcript of Holt McDougal Geometry 12-6 Segment Relationships in Circles 9-6 Segment Relationships in Circles...
Holt McDougal Geometry
12-6Segment Relationships in Circles9-6 Segment Relationships in Circles
Holt GeometryHolt McDougal Geometry
Holt McDougal Geometry
12-6Segment Relationships in Circles
Warm UpSolve for x.
1.
2. 3x = 122
3. BC and DC are tangent to A. Find BC.
Holt McDougal Geometry
12-6Segment Relationships in Circles
In 1901, divers near the Greek island of Antikythera discovered several fragments of ancient items. Using the mathematics of circles, scientists were able to calculate the diameters of the complete disks.
The following theorem describes the relationship among the four segments that are formed when two chords intersect in the interior of a circle.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of x and the length of each chord.
J
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of x and the length of each chord.
Holt McDougal Geometry
12-6Segment Relationships in Circles
In circle A, TS ┴RE. TS= 10 and RE = 3.
a.TE= b. ES =
c. PE= d. PR=
e. Radius of circle A =
Holt McDougal Geometry
12-6Segment Relationships in Circles
The art department is contracted to construct a wooden moon for a play. One of the artists creates a sketch of what it needs to look like by drawing a chord and its perpendicular bisector. Find the diameter of the circle used to draw the outer edge of the moon.
Holt McDougal Geometry
12-6Segment Relationships in Circles
What if…? Suppose the length of chord AB that the archeologists drew was 12 in. What would be the PR?
6 in.
Holt McDougal Geometry
12-6Segment Relationships in Circles
A secant segment is a segment of a secant with at least one endpoint on the circle. An external secant segment is a secant segment that lies in the exterior of the circle with one endpoint on the circle.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of x and the length of each secant segment.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of z and the length of each secant segment.
Holt McDougal Geometry
12-6Segment Relationships in Circles
A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of x.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Find the value of y.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Holt McDougal Geometry
12-6Segment Relationships in Circles
Lesson Quiz: Part I
1. Find the value of d and the length of each chord.
2. Find the diameter of the plate.
Holt McDougal Geometry
12-6Segment Relationships in Circles
Lesson Quiz: Part II
4. Find the value of a.
3. Find the value of x and the length of each secant segment.