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Geometry Basics and Inscribed Circles

Learn about distance equations, midpoint calculation, slope of a line, and angles in inscribed circles. Practice examples provided.

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Geometry Basics and Inscribed Circles

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  1. Warm - up • What is the equation for distance? • How do you find the midpoint between two points? • How do you find the missing endpoint when given and endpoint and the midpoint? • How do you find the slope of a line? • What are your trigonometric ratios?

  2. Inscribed Circles Section: Sol:

  3. In this section we will learn about angles whose vertex is on the circle and whose sides contain chords of the circle. These angles are called ____________ ____________. Inscribed Angles

  4. If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc. Example: If mAC= 60, then mABC= _________ 60

  5. If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent. Example: mABC  mDFE

  6. If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle. Example:

  7. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Example:

  8. Examples: 1. In X, m4 = 7x + 3, m5 = 7x + 3, and m1 = 5x.Find m1, m2, m4, and m5. 2. In A, m1 = 6x + 11, m2 = 9x + 19, m3 = 4y – 25, m4 = 3y – 9, and arc PQ  arc RS. Find m1, m2, m3, and m4. 3. Quadrilateral QRST is inscribed in C. If mT = 95and mS = 100, find mQ and mR.

  9. Suggest Assignments Classwork: Homework: Pg 748 6-20 even, 24

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