![]() One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. In a circle with radius r = 26 cm two parallel chords are drawn. Calculate its radius r.Ĭhord MN of circle has distance from the center circle S 120 cm. The circular sector with a central angle 160° has an area 452 cm². Calculate the magnitude of the central angle that belongs to this chord. There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate both radii and the distance between the two centers o This chord forms an angle of 47° with the radius r1 of the circle c1 and an angle of 24° 30´ with the radius r2 of the circle c2. The common chord of the two circles c1 and c2 is 3.8 cm long. Therefore, ON = 3.We encourage you to watch this tutorial video on this math problem: video1 video2 Related math problems and questions:Ĭalculate the area of a circular line if the radius r = 80 cm and the central angle is α = 110 °? OM can now be found by the use of the Pythagorean Theorem or by recognizing a Pythagorean triple. Therefore, m = 27 ½ and m = 152 ½°.Įxample 5: Use Figure 8, in which AB = 8, CD = 8, and OA = 5, to find ON.įigure 8 A circle with two chords equal in measure.īy Theorem 81, ON = OM. Since m ∠ AOB = 55°, that would make m = 55° and m = 305°. Since OA = 13 and AM = 5, OM can be found by using the Pythagorean Theorem.Īlso, Theorem 80 says that m = m and m = m. įigure 7 A circle with a diameter perpendicular to a chord. In Figure 5, if OX = OY, then by Theorem 82, AB = CD.įigure 5 A circle with two minor arcs equal in measure.Įxample 3: Use Figure 6, in which m = 115°, m = 115°, and BD = 10, to find AC.įigure 6 A circle with two minor arcs equal in measure.Įxample 4: Use Figure 7, in which AB = 10, OA = 13, and m ∠ AOB = 55°, to find OM, m and m. Theorem 82: In a circle, if two chords are equidistant from the center of a circle, then the two chords are equal in measure. In Figure 4, if AB = CD, then by Theorem 81, OX = OY.įigure 4 In a circle, the relationship between two chords being equal in measure and being equidistant from the center. Theorem 81: In a circle, if two chords are equal in measure, then they are equidistant from the center. ![]() įigure 3 A diameter that is perpendicular to a chord. In Figure 3, UT, diameter QS is perpendicular to chord QS By Theorem 80, QR = RS, m = m, and m = m. Theorem 80: If a diameter is perpendicular to a chord, then it bisects the chord and its arcs. These theorems can be used to solve many types of problems. Some additional theorems about chords in a circle are presented below without explanation. ![]() (b) If m = and EF = 8, find GH.įigure 2 The relationship between equality of the measures of (nondiameter) chords and equality of the measures of their corresponding minor arcs. Theorem 79: In a circle, if two minor arcs are equal in measure, then their corresponding chords are equal in measure.Įxample 1: Use Figure 2 to determine the following. The converse of this theorem is also true. Theorem 78: In a circle, if two chords are equal in measure, then their corresponding minor arcs are equal in measure. This is stated as a theorem.įigure 1 A circle with four radii and two chords drawn. This would make m ∠1 = m ∠2, which in turn would make m = m. In Figure 1, circle O has radii OA, OB, OC and OD If chords AB and CD are of equal length, it can be shown that Δ AOB ≅ Δ DOC.
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