Mathematics
In the adjoining figure, O is the center of the circle. If OA = 5 cm, AB = 8 cm and OD ⊥ AB, then length of CD is equal to
2 cm
3 cm
4 cm
5 cm
Circles
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Answer
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
∴ AC = CB = = 4 cm.
In right △OAC,
⇒ OA2 = OC2 + AC2
⇒ 52 = OC2 + 42
⇒ OC2 = 52 - 42
⇒ OC2 = 25 - 16
⇒ OC2 = 9
⇒ OC = = 3 cm.
From figure,
CD = OD - OC = 5 - 3 = 2 cm.
Hence, Option 1 is the correct option.
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Consider the following two statements.
Statement 1: A line which meets a circle in two points is called a secant of the circle.
Statement 2: All radii of a circle are equal.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): Equal chords of a circle are equidistant from centre.
Reason (R): Chords of a circle that are equidistant from the centre of a circle are equal.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).