Question : In the given figure, point O is the centre of a circle of radius 13 cm and AB is a chord perpendicular to OD. If CD = 8 cm, what is the length (in cm) of AB?
Option 1: 6 cm
Option 2: 12 cm
Option 3: 24 cm
Option 4: 28 cm
Correct Answer: 24 cm
Solution : Given, Radius = 13 cm CD = 8 cm ⇒ OC = 13 – 8 = 5 cm [As OD is the radius] In $\triangle AOC$, Using Pythagoras theorem, we get, $AO^2=OC^2+AC^2$ ⇒ $13^2=5^2+AC^2$ ⇒ $AC^2=169-25$ ⇒ $AC=\sqrt{144}$ $\therefore AC = 12$ cm Now, $AB = 2\times AC= 2\times 12 = 24$ cm Hence, the correct answer is 24 cm.
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Question : AB is a chord in a circle of radius 13 cm. From centre O, a perpendicular is drawn through AB intersecting AB at point C. The length of OC is 5 cm. What is the length of AB?
Option 1: 24 cm
Option 3: 20 cm
Option 4: 15 cm
Question : In a given circle, the chord PQ is of length 18 cm. AB is the perpendicular bisector of PQ at M. If MB = 3 cm, then the length of AB is:
Option 1: 27 cm
Option 2: 30 cm
Option 3: 28 cm
Option 4: 25 cm
Question : AB is a chord of a circle having a radius of 1.7 cm. If the distance of this chord AB from the centre of the circle is 0.8 cm, then what is the length (in cm) of the chord AB?
Option 1: 4
Option 2: 1
Option 3: 3
Option 4: 2
Question : Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. PC = 12 cm, and BP = 10 cm, then the length of AB (in m) is:
Option 1: 5.4
Option 2: 6
Option 3: 5
Option 4: 4.4
Question : Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm, and PD = 5 cm, then the length of PB is:
Option 1: 5 cm
Option 2: 7.35 cm
Option 3: 6 cm
Option 4: 4 cm
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