Chapter 6 Quiz. Section 6.1 Circles and Related Segments and Angles

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1 Chapter 6 Quiz Section 6.1 Circles and Related Segments and Angles (1.) TRUE or FALSE: The center of a circle lies in the interior of the circle. For exercises 2 4, use the figure provided. (2.) In O, mabc = 230. What type of arc is ABC? (3.) In O, central angle AOB intercepts AB so that mab = 6 8. Find m AOB. (4.) In O, central angle AOB intercepts AB so that mab = 7 2. Find m ACB. Exercises 2 5 (5.) In O, central angle AOB intercepts AB so that macb = 268. Find mab. (6.) A circle is divided into 8 congruent minor arcs at points R, S, T, V, W, X, Y, and Z in order. Find the measure of the minor arc RS. (7.) TRUE or FALSE: If DF is a diameter of O and DEF is inscribed in O, then m E = 90. (8.) In O ( not shown ) radii OP and OQ form central angle POQ. If OP = 10 and m POQ = 60, find the length of chord PQ. (9.) Points A, B, and C lie on P. If m BC = 27 and mab = 5 6, find mac. (10.) AB is a chord of O and AB = 8. Radius QC is perpendicular to AB at D and QC = 5. Find QD.

2 Section 6.2 More Angle Measures in the Circle (1.) TRUE or FALSE: If AB is tangent to circle O at point T, then OT AB. Use the figure for exercises 2 4. (2.) Chords AB and CD intersect at point E in the interior of P. If m AC = 9 1 and mdb = 5 9, find m CEA. (3.) Chords AB and CD intersect at point E in the interior of P. If m AC = 9 6 and m CEA = 69, find mdb. (4.) Secants AF and CF intersect at point F in the exterior of P. If m AC = 9 6 and m DB = 38, find m F. Exercises 2 4 (5.) TRUE or FALSE: If point X is in the exterior of circle O so that XT is tangent to O, then OX > OT. (6.) If XT is tangent to O at T and TY is a chord, find m XTY if mty = 6 2. Exercises 5 & 6 (7.) Isosceles ABC is inscribed in P so that BA CA. If m B = 35, find mac. (8.) If BA and CA are tangents to P from external point A and mbc = 8 0, find m A. (9.) If BA and CA are tangents to P from external point A and m A = 84, find mbc. Exercises 8 & 9 (10.) Quadrilateral ABCD is inscribed O. How are related? A and C

3 Section 6.3 Line and Segment Relationships in the Circle (1.) In O, radius OA is perpendicular to chord BC at point D. If BC = 10.6, find BD. (2.) For P, tangents BA and BC are drawn from external point B. Also, radii PA and PB are drawn. What type of quadrilateral is PABC? (3.) A circle has radii of length 5 inches. Find the distance from the center of the circle to a chord of length 8 inches. (4.) If two circles are externally tangent, how many common tangents do they have? (5.) In the circle, RS and TQ intersect at V. How are RVT and SVQ related? (6.) TRUE or FALSE: Where RS and TQ intersect at V, it follows that RV VS = TV VQ. (7.) If RV = 12, VS = 9, and TV = 18, find the length of VQ. Exercises 5 7 (8.) Secants AC and CD intersect P at B and E as shown. If AC = 16, CB = 6, and CE = 4, find CD. (9.) Secant AC and tangent CT intersect P as shown. If AC = 9 and CB = 4, find CT. Exercises 8 & 9 (10.) TRUE or FALSE: If A, B, and C lie on a circle, then the center of the circle is the point of intersection of the perpendicular-bisectors of AB and BC.

4 Section 6.4 Some Constructions and Inequalities for the Circle (1.) TRUE or FALSE: If OP is a radius of O, the line constructed perpendicular to OP at point P is tangent to the circle. (2.) Given O with diameter RS, suppose that lines are constructed perpendicular to RS at the endpoints of the diameter. How are the two tangent lines related? (3.) Given that point T lies on P and point N lies in the exterior of P, write an inequality to compare PT and PN. (4.) AB and CD are chords of Q and AB < CD. Which chord lies nearer to center Q? (5.) AB and AC are chords of P and AB < AC. Write an inequality to compare the measures of AOB and m AOC. (6.) Points R, S, T, and V lie on Q. In and TQV, m QRS < m QTV. State an inequality relating mrs and RQS mtv. (7.) If m RQS > m TQV, state an inequality comparing the lengths of RS and TV. Exercises 6 & 7 (8.) Point X lies in the exterior of O. If XT is a tangent to O, state an inequality comparing the lengths of XT and OX. (9.) ABC is inscribed in O so that it separates the circle into three arcs. If m A = 59 and m B = 69, state an inequality comparing the measures of arcs AB, BC, and AC. (10.) In P, the length of the radii are 10. PR is perpendicular to chords AB and CD. If AB = 16 and CD = 12, find EF.

5 Section 6.5 Locus of Points (1.) Describe the locus of points in a plane that are at a distance of 1 inch from a given line. (2.) Name the type of geometric figure that is the locus of points in space that are at a distance of 3 centimeters from the fixed point P. (3.) Name the type of geometric figure that is the locus of points in a plane that are at a distance of 3 centimeters from the fixed point P. (4.) Describe the locus of points in a plane that are equidistant from two distinct points A and B. (5.) Sketch the locus of points in the plane that are midpoints of the radii of circle O. (6.) Describe the locus of points in a plane that are equidistant from the sides of an angle. (7.) Describe the locus of points in a plane that equidistant from 2 parallel lines. (8.) Sketch the locus of points in the plane that are at a distance 1 inch from the 2 given line. (9.) The locus of points in space that are at a distance 2 inches from a fixed point is a sphere. What is the intersection of the sphere and a plane that passes through ( contains ) the center of the sphere? (10.) Consider any two intersecting lines and m. The locus of points equidistant from and m is also a pair of lines p and q. How are p and q related to each other?

6 Section 6.6 Concurrence of Lines (1.) If 3 different lines,, m, and n all contain point A ( intersect at A ), what word characterizes the 3 lines? (2.) TRUE or FALSE: The perpendicular-bisectors of the sides of a triangle are concurrent at a point that is equidistant from the vertices of the triangle. (3.) What is the name of the point at which the altitudes of a triangle are concurrent? (4.) Are the angle-bisectors of a regular hexagon concurrent? (5.) What name is given to the point at which the medians of a triangle are concurrent? (6.) AM, BN, and CP are the medians of ABC. The medians intersect at point X. How are AX and AM related? (7.) For which particular type of quadrilateral will the perpendicularbisectors of the four sides be concurrent rectangle, parallelogram, rhombus, or trapezoid. (8.) TRUE or FALSE: To inscribe a circle in a triangle, the center of the circle is determined by constructing at least two angle-bisectors of the angles in the triangle. (9.) In RST, medians RM, SN, and TP are concurrent at point E. If RE = 18 cm, find RM. (10.) In RST, medians RM, SN, and TP are concurrent at point E. If SN = 30 cm, find SE. Exercises 9 & 10

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