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4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in
BC, CA, AB respectively.
Let BC = 12, AC = 10, AB = 6. Find [P QR].?
BC, CA, AB respectively.
Let BC = 12, AC = 10, AB = 6. Find [P QR].?
Most Upvoted Answer
4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection o...
Given Triangle ABC and Its Properties
- Triangle ABC has sides:
- BC = 12
- AC = 10
- AB = 6
- O is the circumcenter of triangle ABC.
Reflections of the Circumcenter
- Points P, Q, and R are defined as:
- P: Reflection of O in line BC
- Q: Reflection of O in line CA
- R: Reflection of O in line AB
Area Calculation of Triangle PQR
- The area of triangle PQR can be calculated based on its relationship with triangle ABC.
Key Formulas
- The area of triangle ABC, [ABC], can be calculated using Heron's formula:
- Semi-perimeter, s = (AB + AC + BC) / 2 = (6 + 10 + 12) / 2 = 14
- Area, [ABC] = √[s(s - AB)(s - AC)(s - BC)] = √[14(14 - 6)(14 - 10)(14 - 12)]
- [ABC] = √[14 × 8 × 4 × 2] = √[448] = 8√7
Area of Triangle PQR
- The area of triangle PQR is known to be four times the area of triangle ABC:
- Thus, [PQR] = 4 × [ABC] = 4 × 8√7 = 32√7
Final Result
- Therefore, the area of triangle PQR is:
- [PQR] = 32√7
- Triangle ABC has sides:
- BC = 12
- AC = 10
- AB = 6
- O is the circumcenter of triangle ABC.
Reflections of the Circumcenter
- Points P, Q, and R are defined as:
- P: Reflection of O in line BC
- Q: Reflection of O in line CA
- R: Reflection of O in line AB
Area Calculation of Triangle PQR
- The area of triangle PQR can be calculated based on its relationship with triangle ABC.
Key Formulas
- The area of triangle ABC, [ABC], can be calculated using Heron's formula:
- Semi-perimeter, s = (AB + AC + BC) / 2 = (6 + 10 + 12) / 2 = 14
- Area, [ABC] = √[s(s - AB)(s - AC)(s - BC)] = √[14(14 - 6)(14 - 10)(14 - 12)]
- [ABC] = √[14 × 8 × 4 × 2] = √[448] = 8√7
Area of Triangle PQR
- The area of triangle PQR is known to be four times the area of triangle ABC:
- Thus, [PQR] = 4 × [ABC] = 4 × 8√7 = 32√7
Final Result
- Therefore, the area of triangle PQR is:
- [PQR] = 32√7
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4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].?
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4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].?.
4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].?.
Solutions for 4. In 4ABC, let O be the circumcenter. Let P, Q, R be the reflection of O in BC, CA, AB respectively. Let BC = 12, AC = 10, AB = 6. Find [P QR].? in English & in Hindi are available as part of our courses for UPSC.
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