We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byGary Avery
Modified about 1 year ago
Review Ch. 10 Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!
Problem #1 A Find the exact length of arc AB, if circle P has a radius of 18cm. 100° B P
Solution to #1 Arc Length = (100/360) * 36π = (5/18) * 36π = 10π cm.
Problem # 2 Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.
Solution to #2 This is a 9, 40, 41 triangle times 2 so r = 82cm diameter = 164 cm.
Problem #3 Find the radius of a circle with a circumference of
Solution to #3 Circumference = π * diameter so the diameter must be 20 so radius = 10.
Problem #4 Find the measure of arc AE. 210 о x 200 о A B C D E
Solution to #4 *Arc BC = 360 – 210 = 150 о *Angle BDC is supp (tangent-tangent) = 30 о *So Angle ADE = 30 о *So 30 = (1/2)(200 – x) 60 = 200 – x x = 140 о
Problem #5 In the circumscribed polygon, find the length of the AB A B
Solution to #5 AB = 15 – (10 – x) + 12 – x = 5 + x + 12 – x = 17
Problem #6 In circle O, AB is a diameter. OA=3x+5 and OB=2(5x-1). Find AB.
Solution to #6 OA and OB are both radii so are equal. 3x + 5 = 2(5x – 1) 3x + 5 = 10x – 2 7 = 7x 1 = x each radius = 8 ; so diameter AB = 16
Problem #7 Solve for x if and if A B C
Solution to #7 Since angle A is inscribed; 2(5x + 6) = 12x – 2 10x + 12 = 12x – 2 14 = 2x x = 7
Problem #8 MATH is inscribed in the circle. Angle M has a measure of 78 degrees. Find the measure of angle T. M A H T
Solution to #8 Opp. Angles of inscribed quadrilaterals are supp. Measure of Angle T = 180 – 78 = 102 о
Problem #9 Find the radius of the circle if AB is a diameter,, and BC=20. A B C
Solution to #9 *Measure of Angle B = 120/2 = 60 *Measure of Angle C = 90 *30 – 60 – 90 triangle with x = 20 ; so diameter is 2x = 40 *Radius of AB is 20.
Problem #10 A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD. A BC D
Solution to #10 14 – x + 12 – x = 4 26 – 2x = 4 22 = 2x x = 11 So BD = 14 – x = 3
Problem #11 A circle has a radius of 50. How far from the center is a chord of length 28?
Solution to #11 7, 24, 25 right triangle So x = 2 * 24 = 48
Problem #12 A regular octagon is inscribed in a circle. What is the measure of an arc cut off by a side of the octagon?
Solution to #12 * Regular - so all chords congruent. * Congruent chords = congruent arcs. 360/8 = 45 о
Problem #13 Two concentric circles have radii of lengths 16 and 20. Find the length of a chord of the larger circle that is tangent to the smaller circle.
Solution to #13 3, 4, 5 right triangle x = 12 so length of the chord is 24.
Problem #14 A 12 by 10 rectangle is inscribed in a circle. Find the radius.
Solution to # = c = c 2
Problem #15 Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant- secant angle. P 122° 68°
Solution to #15 Angle P = (1/2)(122 – 68) = (1/2)(54) = 27 о
Problem #16 Find the circumference of a circle in which an 80 cm chord is 9 cm from the center.
Solution to #16 9, 40, 41 right triangle so r = 41 C = 2π(41) = 82 π cm
Problem #17 A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x. of circle O O x
Solution to #17 If arc is 5/12 central angle is 5/12 of 360 so central angle is 150 о Radii are congruent so isosceles triangle only 30 о left. Angle x = 30/2 = 15 о
Problem #18 If PA and PB are tangent to circle O at A and B, PA=24, and PO=26, find perimeter of quadrilateral PAOB. P A B O
Solution to #18 OA is perpendicular to PA 5, 12, 13 right triangle. OA = 10 and PB = = 68
Problem #19 Find the measure of angle x. x 92° 44°
Solution to #19
Problem #20 What is the length of a chord that cuts off an arc of 120 degrees in a circle with a radius of 8?
Solution to #20
Problem #21 Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.
Solution to #21
Problem #22 A B C D Circle A has a radius of 5 inches, and circle B has a radius of 20 inches. The centers are 39 inches apart. Find the length of the common external tangent (CD).
Solution to #22
Problem #23 Two tangent segments of a circle with a diameter of 50 inches form a 60 degree angle where they meet at P. How far is P from the center of the circle? 60° P
Solution to #23
Problem #24 AB & AC are tangent to the circle. Find the measure of arc BDC. A B C D 76°
Solution to #24
GEOMETRYGEOMETRY Circle Terminology. Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.
Radius- Is the edge to the middle of the circle. Diameter- It goes throw the whole center of the circle.
GEOMETRYGEOMETRY Circle Terminology Free powerpoints at
A chord that goes through the center of a circle diameter.
Area of Polygons and Circles Chapter Angle Measures in Polygons The sum of the measures of the interior angles of a polygon depends on the number.
Career & Technical Education Drafting – Product Design & Architecture Geometric Construction & Terms.
Section 10.1 Circles Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point.
The Existence of the Nine-Point Circle for a Given Triangle Stephen Andrilli Department of Mathematics and Computer Science La Salle University, Philadelphia,
Circles Chapter Tangents to Circles Circle: the set of all points in a plane that are equidistant from a given point. Center: the given point.
Geometry Honors Section 9.1 Segments and Arcs of Circles.
Honors Geometry Section 5.5 Areas of Regular Polygons.
Other Angle Relationships in Circles Section 10.4 Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.
Date: Sec 10-1 Concept: Tangents to Circles Objective: Given a circle, identify parts and properties as measured by a s.g.
Line A straight path that goes on forever in both directions; it is named by any two points on the line. ZY ZY or YZ.
Section 6.4 Inscribed Polygons U SING I NSCRIBED A NGLES U SING P ROPERTIES OF I NSCRIBED P OLYGONS.
Copyright©amberpasillas2010. Today we are going to find the Area of Parallelograms a nd the Area of Triangles.
10.1 Tangents to Circles Geometry Mr. Davenport Spring 2010.
A triangle with at least two sides congruent is called an Isosceles Triangle. bc a In this triangle, sides b and c are congruent.
LG 4-4 Arc Length. Arc Length An arc of a circle is a segment of the circumference of the circle.
Quantitative Methods Area & Perimeter of Plane figures Pranjoy Arup Das.
Circle Theory. 2x2x x This is the ARC o Centre of Circle The Angle x subtended at the centre of a circle by an arc is twice the size of the angle on the.
Find the sum of the measures of the angles in an octagon. 4. A pentagon has two right angles, a 100° angle and a 120° angle. What is the measure.
Parts of a Circle Aim: To understand and know the vocabulary for parts of a circle.
Teach GCSE Maths Alternate Segment Theorem. Teach GCSE Maths Alternate Segment Theorem © Christine Crisp "Certain images and/or photos on this presentation.
FeatureLesson Geometry Lesson Main Find the values of the variables for which GHIJ must be a parallelogram x = 6, y = 0.75 a = 34, b = 26 Proving.
All about Shapes Properties of Shapes Number of sides Number of angles Number of lines of symmetry Regular or irregular Right Angles Parallel lines.
FeatureLesson Geometry Lesson Main PA and PB are tangent to C. Use the figure for Exercises 1–3. 1.Find the value of x. 2.Find the perimeter of quadrilateral.
6.G.1 Perimeter and Area of Rectangles, Squares and Triangles.
Honors Geometry Section 5.2 Areas of Triangles and Quadrilaterals.
© 2016 SlidePlayer.com Inc. All rights reserved.