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A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal to
Correct answer is '4'. Can you explain this answer?
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A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The tr...
The centroid G of triangle is collinear with H and O, and G lies two thirds of way from A to M. Therefore H is two thirds of the way from A to F, so AF = 3 × OM = 15.
Since the triangle BFH and AFC are similar, hence,
⇒ BF. FC = FH.AF = 75.
Now, BC2 = (BF + FC)2 = (BF – FC)2 + 4BF.FC
But, FC – BF = (FM + MC) – (BM – FM) = 2FM = 2 HO = 22
Since the triangle BFH and AFC are similar, hence,
⇒ BF. FC = FH.AF = 75.
Now, BC2 = (BF + FC)2 = (BF – FC)2 + 4BF.FC
But, FC – BF = (FM + MC) – (BM – FM) = 2FM = 2 HO = 22
Most Upvoted Answer
A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The tr...
To solve this problem, we need to use the properties of a rectangle and the relationships between the sides and angles of a triangle. Let's break down the problem into smaller steps:
Step 1: Analyzing the rectangle
We are given a rectangle HOMF, where HO = 11 and OM = 5. Since it is a rectangle, the opposite sides are equal in length. Therefore, HM = OF = 11 and HO = MF = 5.
Step 2: Understanding the triangle ABC
The triangle ABC is formed by joining the orthocenter H, circumcenter O, and the midpoint of BC, M. The foot of the altitude from A is labeled as F.
Step 3: Finding the length of BC
To find the length of BC, we need to use the properties of a rectangle. Since HM = OF = 11, we can determine that BC = 2 * HM = 2 * 11 = 22.
Step 4: Finding the length of AF
To find the length of AF, we can use the Pythagorean theorem. In a right-angled triangle AOF, AO is the radius of the circumcircle, which is equal to HO = 11. The length of OF is given as 5. Therefore, AF can be found using the Pythagorean theorem:
AF^2 = AO^2 - OF^2
AF^2 = 11^2 - 5^2
AF^2 = 121 - 25
AF^2 = 96
AF = √96 = 4√6
Step 5: Finding l/7
We are asked to find l/7, where l is the length of BC. From step 3, we found that BC = 22. Therefore, l/7 = 22/7 = 3.14.
Step 6: Final answer
The correct answer is given as 4. However, our calculation in step 5 gives us 3.14. It seems there might be a mistake in either the given answer or our calculations. Please double-check the given answer or provide additional information to proceed further.
Please note that the provided solution is based on the given information and may vary if there are any additional constraints or details to consider.
Step 1: Analyzing the rectangle
We are given a rectangle HOMF, where HO = 11 and OM = 5. Since it is a rectangle, the opposite sides are equal in length. Therefore, HM = OF = 11 and HO = MF = 5.
Step 2: Understanding the triangle ABC
The triangle ABC is formed by joining the orthocenter H, circumcenter O, and the midpoint of BC, M. The foot of the altitude from A is labeled as F.
Step 3: Finding the length of BC
To find the length of BC, we need to use the properties of a rectangle. Since HM = OF = 11, we can determine that BC = 2 * HM = 2 * 11 = 22.
Step 4: Finding the length of AF
To find the length of AF, we can use the Pythagorean theorem. In a right-angled triangle AOF, AO is the radius of the circumcircle, which is equal to HO = 11. The length of OF is given as 5. Therefore, AF can be found using the Pythagorean theorem:
AF^2 = AO^2 - OF^2
AF^2 = 11^2 - 5^2
AF^2 = 121 - 25
AF^2 = 96
AF = √96 = 4√6
Step 5: Finding l/7
We are asked to find l/7, where l is the length of BC. From step 3, we found that BC = 22. Therefore, l/7 = 22/7 = 3.14.
Step 6: Final answer
The correct answer is given as 4. However, our calculation in step 5 gives us 3.14. It seems there might be a mistake in either the given answer or our calculations. Please double-check the given answer or provide additional information to proceed further.
Please note that the provided solution is based on the given information and may vary if there are any additional constraints or details to consider.
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A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer?
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A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer?.
A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer?.
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A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer?, a detailed solution for A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? has been provided alongside types of A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal toCorrect answer is '4'. Can you explain this answer? theory, EduRev gives you an
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