13. In the figure, if OA = 5 cm, AB = 8 cm and OD 1 AB then. Find CD.
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where is the figure mate
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Answer:
CD = 2 cm
Step-by-step explanation:
Radius of the circle = r = AO = 5 cm
Length of chord AB = 8 cm
∴ AC = 1/2(AB) = 8/2 = 4 cm
In right angled triangle AOC.
(AO)^2 = (OC)^2 + (AC)^2
=> (5)^2 = (OC)^2 + (4)^2
=> (OC)^2 = (5)2 - (4)^2
=> (OC)^2 = 25 - 16
=> (OC)^2 = 9
=> OC = 3 cm
∴ The distance of AC from the center of the circle is 3 cm.
Now, OD is the radius of the circle,
Thus, OD = 5 cm
∴ CD = OD - OC
=> CD = 5 - 3
=> CD = 2 cm
=> CD = 2 cm
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