University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

360

Pages:

3
Author:

efreet4ifh37v

Study Guide 10.1 Lines and Segments that Intersect Circles Know the definition of the words!!! marks are very important Tell whether the common tangent is internal or external Name the circle Name the two radii Name two chords Name a diameter Name a secant Name a tangent Find the variable 3x - 4 = 2x + 1 15^2 + 8^2 = (x + 8)^2 two tangent lines crossing the same exterior point create congruent segments tangent lines will create 90° angles with a circle's radius Find AB 5^2 + 12^2 = AB^2 144 + 25 = AB^2 169 = AB^2 AB = 13 10.2 Finding Arc Measures major - longer arc minor - shorter arc semicircle - half of the circle circles = 360° Classify the arc named: QRS - semicircle TS - minor TPS - major PQ - minor Are the arcs congruent? Explain NM and OP - No, the circles are not congruent. AC and CD - Yes, the central angles are congruent. Find the measure of each arc: AC - 135° DAB - 225° QR - 54° 10.3 Using Chords diameters always bisect chords create equal parts across the chord all radii in a circle are congruent congruent chords are always equidistant to the center at 90° angles Find the variables 6x + 5 = 11 3^2 + 4^2 = h^2 4x + 1 = x + 8 In the diagram of OR, determine if the statement is true or false. Explain your decision. PQ = QN - Yes NL = LP - Yes MN = MP - Yes PN = PL - No 10.4 Inscribed Angles and Polygons inscribed angles = 1/2 arc if a quadrilateral is inscribed in a circle, then opposite angles are supplementary Find the variable x = 1/2(70) y + 80 = 180 x + 80 + 70 + 135 = 360 70 + 110 + x + 150 = 360 x + 90 + 40 = 180 10.5 Angle Relationships in Circles exterior angle + central angle = 180 Find the variable: x = 1/2(arc) 40 + x = 180 9x = 1/2(arc) 2x + 114 = 180 x = 1/2(70+10) 10.6 Segment Relationships in Circles (part)(part) = (part)(part) Find the variable: 6(6) = 5(5+x) 6(6) = x(x+9) 5(5+x) = 7(7) 10.7 Circles in the Coordinate Plane Write the equation of the circle. Center (0,0), radius=4 (x-0)^2 + (y-0)^2 = 4^2 x^2 + y^2 = 16 Find the radius and center of the circle. x^2 + y^2 = 16 Center (0,0), radius=4 Write the equation of a circle with center (7,-2) and radius=5. (x-7)^2 + (y+2)^2 = 5^2 (x-7)^2 + (y+2)^2 = 25 Graph the equation. (x-4)^2 + (y+3)^2 = 36 Center (4,-3), radius=6