Question : A chord of the larger among two concentric circles is of length 10 cm and it is tangent to the smaller circle. What is the area (in cm2) of the annular portion between the two circles?
Option 1: $10 \pi$
Option 2: $25 \pi$
Option 3: $5 \pi$
Option 4: $\frac{5 \pi}{2}$
Correct Answer: $25 \pi$
Solution :
Let the radius of the bigger circle be 'R' and the smaller circle be 'r'. Let AB be a chord of the bigger circle that is tangent to the smaller circle. ⇒ AB = 10 cm ⇒ AM = $\frac{10}{2}$ = 5 cm In triangle OAM ⇒ OA2 = OM2 + AM2 ⇒ R2 = r2 + 52 ⇒ R2 – r2 = 25 Area between the two circle = $\pi(R^2 - r^2) = 25 \pi$ cm2 Hence, the correct answer is $ 25 \pi$.
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Question : Two concentric circles are drawn with radii 12 cm and 13 cm. What will be the length of any chord of the larger circle that is tangent to the smaller circle?
Option 1: 5 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 25 cm
Question : Two circles of diameters 10 cm and 6 cm have the same centre. A chord of the larger circle is a tangent of the smaller one. The length of the chord is:
Option 1: 4 cm
Option 3: 6 cm
Option 4: 10 cm
Question : Out of two concentric circles, the radius of the outer circle is 6 cm and the chord PQ of the length 10 cm is a tangent to the inner circle. Find the radius (in cm) of the inner circle.
Option 1: $4$
Option 2: $\sqrt{7}$
Option 3: $\sqrt{13}$
Option 4: $\sqrt{11}$
Question : The circumference of a circle exceeds its diameter by 60 cm. The area of the circle is: (Take $\pi=\frac{22}{7}$ )
Option 1: 1078 cm2
Option 2: 616 cm2
Option 3: 536 cm2
Option 4: 346.5 cm2
Question : The area of a circle is 1386 cm2. What is the radius of the circle? [Use $\pi= \frac{22}{7}$]
Option 1: 7 cm
Option 2: 14 cm
Option 3: 18 cm
Option 4: 21 cm
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