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ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is?
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ABC is a right angled triangle right angled at b such that BC = 6 cm a...
Understanding the Triangle
Given triangle ABC is right-angled at B, with the sides as follows:
- BC = 6 cm (one leg)
- AB = 8 cm (another leg)
To find the radius of the inscribed circle (inradius) for triangle ABC, we first need to determine the area and the semi-perimeter of the triangle.
Calculating the Area
- The area (A) of a right-angled triangle can be calculated using the formula:
- A = (1/2) * base * height
- Here, base = BC = 6 cm, and height = AB = 8 cm.
- Therefore, the area:
- A = (1/2) * 6 * 8 = 24 cm²
Calculating the Semi-Perimeter
- The semi-perimeter (s) is calculated as:
- s = (a + b + c) / 2
- Where a = AB, b = BC, and c = AC (the hypotenuse).
- First, we need to calculate AC using the Pythagorean theorem:
- AC = √(AB² + BC²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.
- Now, we can find the semi-perimeter:
- s = (8 + 6 + 10) / 2 = 12 cm.
Calculating the Inradius
- The formula for the radius (r) of the inscribed circle is given by:
- r = A / s
- Substituting the values:
- r = 24 cm² / 12 cm = 2 cm.
Conclusion
- The radius of the inscribed circle in triangle ABC is 2 cm.
Given triangle ABC is right-angled at B, with the sides as follows:
- BC = 6 cm (one leg)
- AB = 8 cm (another leg)
To find the radius of the inscribed circle (inradius) for triangle ABC, we first need to determine the area and the semi-perimeter of the triangle.
Calculating the Area
- The area (A) of a right-angled triangle can be calculated using the formula:
- A = (1/2) * base * height
- Here, base = BC = 6 cm, and height = AB = 8 cm.
- Therefore, the area:
- A = (1/2) * 6 * 8 = 24 cm²
Calculating the Semi-Perimeter
- The semi-perimeter (s) is calculated as:
- s = (a + b + c) / 2
- Where a = AB, b = BC, and c = AC (the hypotenuse).
- First, we need to calculate AC using the Pythagorean theorem:
- AC = √(AB² + BC²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.
- Now, we can find the semi-perimeter:
- s = (8 + 6 + 10) / 2 = 12 cm.
Calculating the Inradius
- The formula for the radius (r) of the inscribed circle is given by:
- r = A / s
- Substituting the values:
- r = 24 cm² / 12 cm = 2 cm.
Conclusion
- The radius of the inscribed circle in triangle ABC is 2 cm.
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ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is?
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ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is?.
ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a right angled triangle right angled at b such that BC = 6 cm and ab = 8 cm. a circle with centre OS inscribed in triangle abc. the radius of the circle is?.
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