(a) The diagram shows a circle, centre 0. AB and CD are chord.
Given that OM = 8 cm, NT = 3 cm, AB = 30 cm.

(1) Calculate the radius
(2) Calculate the length of CD​

(a) The Diagram Shows A Circle, Centre 0. AB And CD Are Chord.Given That OM = 8 Cm, NT = 3 Cm, AB = 30

Answers

Answer 1

Answer:

1) Radius = 17 cm

2). CD = 19.3 cm

Step-by-step explanation:

1). O is the center of the given circle.

 By joining the center and point A located at the circumference of the circle,

 OA = radius of the circle.

 Length of chord AB = 30 cm

 "Line from the center of a circle to the chord inside the circle is a perpendicular bisector of the chord"

  By the given property, OM equally divides the chord AB.

 AM = MB

 AM = [tex]\frac{1}{2}(AB)[/tex]

 AM = [tex]\frac{10}{2}[/tex] = 5 cm

 By applying Pythagoras theorem in ΔOAM,

 AO² = OM² + AM²

 AO² = 8² + 15²

 AO =  √289

 AO = 17 cm

 Therefore, radius of the circle = 17 cm

2). Since, OT, OC and OA are the radii of the given circle,

  OT = OC = OA = 17 cm

  ON = OT - NT

         = 17 - 3

         = 14 cm

   By applying Pythagoras theorem in ΔOCM,

   OC² = ON² + CN²

   17² = 14² + CN²

   CN = [tex]\sqrt{(17^2-14^2)}[/tex]

         = [tex]\sqrt{93}[/tex]

         = 9.64 cm

     Since, CD = 2(CN)

      CD = 2 × 9.64

             = 19.29 cm

              ≈ 19.3 cm

(a) The Diagram Shows A Circle, Centre 0. AB And CD Are Chord.Given That OM = 8 Cm, NT = 3 Cm, AB = 30

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Step-by-step explanation:

[tex]4x^2 - 3 = 3x^2 + 13 \\ \\ 4x^2 - 3 - 3x^2 - 13 = 0 \\ \\ 4 {x}^{2} - 3 {x}^{2} - 16 = 0 \\ \\ {x}^{2} - 16 = 0 \\ \\ {x}^{2} - {(4)}^{2} = 0 \\ \\ (x + 4)(x - 4) = 0 \\ \\ x + 4 = 0 \: \: or \: \: x - 4 = 0 \\ \\ x = - 4 \: \: or \: \: x = 4 \\ \\ x = - 4, \: \: 4[/tex]

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Answers

Answer:

[tex]\displaystyle m=-2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

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Step-by-step explanation:

Step 1: Define

Point (0, 0)

Point (5, -10)

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Let "m" be the slope of the line passing through the point.

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