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Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is
Correct answer is option 'D'. Can you explain this answer?
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Two circles, each of radius 4 cm, touch externally. Each of these two ...
Let 'h’ be the height of the triangle ABC, semi perimeter(S) = (4+4+r+4+4+r)/2 = 8 + r,
a=4 +r, b = 4 + r, c = 8
Height (h) = √(8+r)r
Now, h + r = 4
(Considering the height of the triangle)
Alternatively,
AE2 + EC2 = AC2⟶ 42 + (4 − r)2 = (4 + r)2⟶⟶⟶ r = 1
Most Upvoted Answer
Two circles, each of radius 4 cm, touch externally. Each of these two ...
To solve this problem, let's consider the given information step by step.
Step 1: Drawing the Diagram
We start by drawing the two circles that touch externally. Let's label them as Circle A and Circle B.
Step 2: Drawing the Third Circle
We draw a third circle that touches both Circle A and Circle B externally. Let's label this circle as Circle C.
Step 3: Identifying the Common Tangent
The question states that the three circles have a common tangent. Let's draw this tangent.
Step 4: Identifying the Radii
We are given that the radii of Circle A and Circle B are both 4 cm. Let's label these radii as r.
Step 5: Identifying the Radii of Circle C
To find the radius of Circle C, we need to use the property of externally tangent circles.
Step 6: Identifying the Distance between the Centers
The distance between the centers of Circle A and Circle B is equal to the sum of their radii, which is 8 cm.
Step 7: Identifying the Distance between the Center of Circle C and the Common Tangent
The distance between the center of Circle C and the common tangent is equal to the radius of Circle C.
Step 8: Applying the Property of Externally Tangent Circles
According to the property of externally tangent circles, the distance between their centers is equal to the sum of their radii.
Step 9: Solving for the Radius of Circle C
Using the information from steps 6 and 7, we can write the equation:
8 cm = 4 cm + r
Simplifying the equation, we get:
r = 4 cm
Therefore, the radius of the third circle (Circle C) is 4 cm. Hence, the correct answer is option D.
Step 1: Drawing the Diagram
We start by drawing the two circles that touch externally. Let's label them as Circle A and Circle B.
Step 2: Drawing the Third Circle
We draw a third circle that touches both Circle A and Circle B externally. Let's label this circle as Circle C.
Step 3: Identifying the Common Tangent
The question states that the three circles have a common tangent. Let's draw this tangent.
Step 4: Identifying the Radii
We are given that the radii of Circle A and Circle B are both 4 cm. Let's label these radii as r.
Step 5: Identifying the Radii of Circle C
To find the radius of Circle C, we need to use the property of externally tangent circles.
Step 6: Identifying the Distance between the Centers
The distance between the centers of Circle A and Circle B is equal to the sum of their radii, which is 8 cm.
Step 7: Identifying the Distance between the Center of Circle C and the Common Tangent
The distance between the center of Circle C and the common tangent is equal to the radius of Circle C.
Step 8: Applying the Property of Externally Tangent Circles
According to the property of externally tangent circles, the distance between their centers is equal to the sum of their radii.
Step 9: Solving for the Radius of Circle C
Using the information from steps 6 and 7, we can write the equation:
8 cm = 4 cm + r
Simplifying the equation, we get:
r = 4 cm
Therefore, the radius of the third circle (Circle C) is 4 cm. Hence, the correct answer is option D.
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Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer?
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Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer?.
Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, isCorrect answer is option 'D'. Can you explain this answer?.
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