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For 2 Concentric circles, a chord of the larger circle is a tangent to the smaller circle. If the chord length is 16 cm and radius of the smaller circle is 6 cm, what is the radius of the larger circle?
- a)8 cm
- b)10 cm
- c)9 cm
- d)12 cm
- e)16 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For 2 Concentric circles, a chord of the larger circle is a tangent t...
Since, perpendicular line joining the centre of a circle to a chord bisects the chord, ∴ AB = 16/2 = 8 cm.
Radius of the smaller circle = OA = 6 cm.
Radius of the larger circle = OB.
In ∆AOB, applying Pythagoras' Theorem,
OB2 = OA2 + AB2
∴ OB = √62+82) = 10 cm.
Most Upvoted Answer
For 2 Concentric circles, a chord of the larger circle is a tangent t...
Problem:
For two concentric circles, a chord of the larger circle is a tangent to the smaller circle. If the chord length is 16 cm and the radius of the smaller circle is 6 cm, what is the radius of the larger circle?
Solution:
Let's consider the given information and solve the problem step by step:
Step 1: Understanding the problem
We have two concentric circles, which means they share the same center point. A chord of the larger circle is a line segment that connects two points on the circumference of the larger circle. In this case, the chord is also tangent to the smaller circle, meaning it touches the smaller circle at exactly one point.
Step 2: Identifying the given information
We are given the length of the chord, which is 16 cm, and the radius of the smaller circle, which is 6 cm.
Step 3: Drawing a diagram
To visualize the problem, let's draw a diagram of the two concentric circles with the chord and the tangent point on the smaller circle.
Step 4: Applying the properties of tangents and chords
In a circle, a line tangent to the circle is perpendicular to the radius drawn to the point of tangency. This property helps us solve the problem.
Step 5: Finding the distance between the chord and the center of the smaller circle
Since the chord is tangent to the smaller circle, it is perpendicular to the radius drawn to the point of tangency. This means the distance between the chord and the center of the smaller circle is equal to the radius of the smaller circle, which is 6 cm.
Step 6: Dividing the chord into two equal parts
Since the chord is tangent to the smaller circle, it divides the chord into two equal parts. Therefore, each part of the chord is half the length of the chord, which is 16 cm/2 = 8 cm.
Step 7: Finding the radius of the larger circle
The radius of the larger circle is the sum of the radius of the smaller circle and the distance between the chord and the center of the smaller circle. In this case, it is 6 cm + 6 cm = 12 cm.
Therefore, the radius of the larger circle is 12 cm.
Conclusion:
The radius of the larger circle is 12 cm (option B).
For two concentric circles, a chord of the larger circle is a tangent to the smaller circle. If the chord length is 16 cm and the radius of the smaller circle is 6 cm, what is the radius of the larger circle?
Solution:
Let's consider the given information and solve the problem step by step:
Step 1: Understanding the problem
We have two concentric circles, which means they share the same center point. A chord of the larger circle is a line segment that connects two points on the circumference of the larger circle. In this case, the chord is also tangent to the smaller circle, meaning it touches the smaller circle at exactly one point.
Step 2: Identifying the given information
We are given the length of the chord, which is 16 cm, and the radius of the smaller circle, which is 6 cm.
Step 3: Drawing a diagram
To visualize the problem, let's draw a diagram of the two concentric circles with the chord and the tangent point on the smaller circle.
Step 4: Applying the properties of tangents and chords
In a circle, a line tangent to the circle is perpendicular to the radius drawn to the point of tangency. This property helps us solve the problem.
Step 5: Finding the distance between the chord and the center of the smaller circle
Since the chord is tangent to the smaller circle, it is perpendicular to the radius drawn to the point of tangency. This means the distance between the chord and the center of the smaller circle is equal to the radius of the smaller circle, which is 6 cm.
Step 6: Dividing the chord into two equal parts
Since the chord is tangent to the smaller circle, it divides the chord into two equal parts. Therefore, each part of the chord is half the length of the chord, which is 16 cm/2 = 8 cm.
Step 7: Finding the radius of the larger circle
The radius of the larger circle is the sum of the radius of the smaller circle and the distance between the chord and the center of the smaller circle. In this case, it is 6 cm + 6 cm = 12 cm.
Therefore, the radius of the larger circle is 12 cm.
Conclusion:
The radius of the larger circle is 12 cm (option B).
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For 2 Concentric circles, a chord of the larger circle is a tangent to the smaller circle. If the chord length is 16 cm and radius of the smaller circle is 6 cm, what is the radius of the larger circle?a)8 cmb)10 cmc)9 cmd)12 cme)16 cmCorrect answer is option 'B'. Can you explain this answer?
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