Mathematics
Assertion (A) : If a circle is of radius 8 cm and the length of its minor arc is also 8 cm, then the length of major arc = 8(2π - 1) cm.
Reason (R) : For every circle, sum of the length of its major arc and length of its minor arc is equal to the circumference of the circle.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Circles
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Answer
Given, radius of a circle = 8 cm and the length of its minor arc = 8 cm
Circumference of the circle = 2πr = 2 x π x 8 = 16π
We know that,
Length of minor arc + length of major arc = Circumference of the circle
So, reason (R) is true.
⇒ 8 + length of major arc = 16π
⇒ length of major arc = 16π - 8
⇒ length of major arc = 8(2π - 1) cm
So, assertion (A) is true.
∴ Both A and R are correct, and R is the correct explanation for A.
Hence, option 1 is the correct option.
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The following figure shows the circle with centre O.
Use the figure to fill the blanks in each of the following :
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