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Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)
- a)9/16
- b)9/25
- c)4/25
- d)16/25
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Let C1 and C2 be the inscribed and circumscribed circles of a triangle...
Let ΔABC has three sides BC, AB and AC equal to 3 cm, 4 cm and 5 cm respectively.
Now, as, (5)2 = (3)2 + (4)2 i.e. (AC)2 = (AB)2 + (BC)2
∴ ΔABC is a right angle triangle
Then, for circumcircle C2, radius = AC/2 = 5/2 = 2.5
Most Upvoted Answer
Let C1 and C2 be the inscribed and circumscribed circles of a triangle...
Let ΔABC has three sides BC, AB and AC equal to 3 cm, 4 cm and 5 cm respectively.
Now, as, (5)2 = (3)2 + (4)2 i.e. (AC)2 = (AB)2 + (BC)2
∴ ΔABC is a right angle triangle
Then, for circumcircle C2, radius = AC/2 = 5/2 = 2.5
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Community Answer
Let C1 and C2 be the inscribed and circumscribed circles of a triangle...
Given:
- The sides of the triangle are 3 cm, 4 cm, and 5 cm.
- C1 is the inscribed circle and C2 is the circumscribed circle of the triangle.
To find:
The ratio of the areas of C1 to C2.
Solution:
Step 1: Find the radius of C1:
Since C1 is the inscribed circle, the radius of C1 is given by the formula:
radius of C1 = (area of triangle) / (semiperimeter of triangle)
The semiperimeter of the triangle can be calculated using the formula:
semiperimeter of triangle = (3 + 4 + 5) / 2 = 6 cm
The area of the triangle can be calculated using Heron's formula:
area of triangle = √(semiperimeter * (semiperimeter - side1) * (semiperimeter - side2) * (semiperimeter - side3))
= √(6 * (6 - 3) * (6 - 4) * (6 - 5))
= √(6 * 3 * 2 * 1)
= √(36)
= 6 cm^2
Therefore, the radius of C1 = 6 cm / 6 cm = 1 cm.
Step 2: Find the radius of C2:
Since C2 is the circumscribed circle, the radius of C2 is given by the formula:
radius of C2 = (side1 * side2 * side3) / (4 * (area of triangle))
= (3 * 4 * 5) / (4 * 6)
= (60) / (24)
= 5/2 cm.
Step 3: Find the ratio of the areas of C1 to C2:
The area of a circle is given by the formula:
area of circle = π * (radius)^2
The ratio of the areas of C1 to C2 is therefore:
(area of C1) / (area of C2) = (π * (radius of C1)^2) / (π * (radius of C2)^2)
= (π * (1 cm)^2) / (π * (5/2 cm)^2)
= 1 / (25/4)
= 4/25
Answer:
The ratio of the areas of C1 to C2 is 4/25. Therefore, the correct answer is option 'C'.
- The sides of the triangle are 3 cm, 4 cm, and 5 cm.
- C1 is the inscribed circle and C2 is the circumscribed circle of the triangle.
To find:
The ratio of the areas of C1 to C2.
Solution:
Step 1: Find the radius of C1:
Since C1 is the inscribed circle, the radius of C1 is given by the formula:
radius of C1 = (area of triangle) / (semiperimeter of triangle)
The semiperimeter of the triangle can be calculated using the formula:
semiperimeter of triangle = (3 + 4 + 5) / 2 = 6 cm
The area of the triangle can be calculated using Heron's formula:
area of triangle = √(semiperimeter * (semiperimeter - side1) * (semiperimeter - side2) * (semiperimeter - side3))
= √(6 * (6 - 3) * (6 - 4) * (6 - 5))
= √(6 * 3 * 2 * 1)
= √(36)
= 6 cm^2
Therefore, the radius of C1 = 6 cm / 6 cm = 1 cm.
Step 2: Find the radius of C2:
Since C2 is the circumscribed circle, the radius of C2 is given by the formula:
radius of C2 = (side1 * side2 * side3) / (4 * (area of triangle))
= (3 * 4 * 5) / (4 * 6)
= (60) / (24)
= 5/2 cm.
Step 3: Find the ratio of the areas of C1 to C2:
The area of a circle is given by the formula:
area of circle = π * (radius)^2
The ratio of the areas of C1 to C2 is therefore:
(area of C1) / (area of C2) = (π * (radius of C1)^2) / (π * (radius of C2)^2)
= (π * (1 cm)^2) / (π * (5/2 cm)^2)
= 1 / (25/4)
= 4/25
Answer:
The ratio of the areas of C1 to C2 is 4/25. Therefore, the correct answer is option 'C'.
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Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer?
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Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer?.
Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)a)9/16b)9/25c)4/25d)16/25Correct answer is option 'C'. Can you explain this answer?.
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