Name: _____________________________________________ Date:____________ Math 424 First Test Fourth Quarter Show all work for full credit. Partial credit may be awarded for correctly shown work. 1. Complete each statement with always A, 2. Each of three congruent circles has a radius sometimes S, or never N to make the of 1, and each is externally tangent to the statement true. other two. An equilateral triangle circum- a. An inscribed angle which intercepts an arc scribes the circles, so that each circle is whose measure is less than 180 is _____ an tangent to two of the sides of the triangle. obtuse angle. What is the perimeter of the triangle? b. The center of the circle circumscribed about a triangle ___ lies in the interior region of the triangle. c. If the perpendiculars drawn from the center of a circle upon two chords are congruent, then the minor arcs intercepted by these chords are ____ equal. d. Two right triangles inscribed in the same or congruent circles are _____ congruent. e. If two angles intercept the same arc of a cir- cle, they are ___ congruent. 3. In the accompanying diagram, chord AB is 4. ABCD is a square inscribed in O and the perpendicular bisector of radius OC. If AB 8. Find the area of the shaded region. C AB12, find OC. A E B O 5. In the accompanying figure, CDA and CEB are secants drawn from external point C. Chords AE and BD intersect at N. If m C 40, m ANB 100, mAB 5 x 8 y , and mDE3 x 2 y 4, find the values of x,and y. A D C N E B 6. In O of the accompanying figure, PQR is a secant to O . Q and S are points on O. If PQ4, RQ 10, and PO 15, find PS. Q R P S O 7. In the accompanying diagram of O,PBOA is a secant, PT is tangent to O at T, m P40, and QB AT. A Find: a) m BOT Q b) m ATO O c) m PBQ T B P 8. Given: AC is tangent to O at A. Prove: AD AB BD CA A O B C D Choose the most appropriate answer choice for each question below. Write the numerical answer choice in the space provided. No partial credit will be awarded in this section. 1. Around which of the following polygons can you always circumscribe a circle? I. triangle II. parallelogram III. rhombus IV. rectangle 1 I only 3 II and III only 2 I and IV only 4 I and II only 5 I, II, and IV only 1. ______ 2. Suppose you are given OXOX and on . You draw a diameter through , intersecting O at W. You then draw a W with radius OW, intersecting O at Y and Z. Which of the following describes figure XYZ ? 1 An isosceles triangle inscribed in O. 2 An equilateral triangle inscribed in O. 3 An isosceles triangle circumscribed aboutO . 4 An equilateral triangle circumscribed about O. 5 None of the above. 2. ________ 3. FGHG and are tangent to the smaller circle at PQ and respectively. If mFHymPQx and , which of the following expresses yx in terms of ? 1 y 180 x 3 y 360 2 x F P 2 yx 180 4 yx 2 360 5 Cannot be determined by the information given. G 3. ________ Q H 4. To find the center of the circle passing through three given noncollinear points, you would find the intersection of what two items? 1 Two altitudes 3 Two angle bisectors 2 Two medians 4 Two perpendicular bisectors 5 None of the above. 4. _____.