(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

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 =

 AM = = 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 =

         =

         = 9.64 cm

     Since, CD = 2(CN)

      CD = 2 × 9.64

             = 19.29 cm

              ≈ 19.3 cm

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step-by-step explanation: