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
