Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 1: 10 cm
Option 2: 13 cm
Option 3: 12 cm
Option 4: 24 cm
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Correct Answer: 13 cm
Solution : AB = 24 cm And OC = 5 cm We have to find AO. C is the middle point of the chord. $\therefore$ AC = $\frac{24}{2} = 12\ \mathrm{cm}$ Using Pythagoras theorem, $\text{AO}^2 = \text{AC}^2 + \text{OC}^2$ ⇒ $\text{AO}^2 = 12^2 + 5^2$ ⇒ $\text{AO}^2 = 144 + 25$ ⇒ $\text{AO}^2 = 169$ ⇒ $\text{AO} = 13\ \mathrm{cm}$ Hence, the correct answer is 13 cm.
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Question : The radius of a circle is 5 cm. The length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?
Option 1: 4 cm
Option 2: 5 cm
Option 3: 6 cm
Option 4: 8 cm
Question : The radius of a circle is 10 cm. The angle made by chord AB at the centre of this circle is 60°. What is the length of this chord?
Option 1: 40 cm
Option 2: 20 cm
Option 3: 30 cm
Option 4: 10 cm
Question : In a circle, a 14 cm long chord is 24 cm from the centre of the circle. Find the length of the radius of the circle.
Option 1: 30 cm
Option 2: 25 cm
Option 3: 50 cm
Option 4: 27 cm
Question : A chord of length 40 cm is drawn in a circle having a diameter of 50 cm. What is the a minimum distance of another parallel chord of length 30 cm in the same circle from a 40 cm long chord?
Option 2: 15 cm
Option 3: 5 cm
Option 4: 20 cm
Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
Option 1: $5 \sqrt{5}$ cm
Option 2: $5 \sqrt{2}$ cm
Option 3: $5$ cm
Option 4: $5 \sqrt{3}$ cm
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