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In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not
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In triangle ABC, if x and y are points on AB and AC respectively such ...
To solve this problem, we need to use the concept of similar triangles.
Let's call the point of intersection between XY and BC as Z.
Since AX/XB = 3/4, we can say that AZ/ZB = 3/4. Similarly, we can say that AY/YC = 5/5 = 1.
Now, let's consider triangles AZX and CZY.
Since the corresponding sides of these triangles are proportional (AZ/ZC = 3/1 and AX/XY = 3/3 = 1), we can conclude that these triangles are similar.
Using the concept of similar triangles, we know that the ratio of the lengths of corresponding sides is the same.
Therefore, we can say that AZ/ZY = 3/1.
Now, we know that AY = 5, so AZ = AY - ZY = 5 - ZY.
Substituting this value in the equation AZ/ZY = 3/1, we get (5 - ZY)/ZY = 3/1.
Cross-multiplying, we get 5 - ZY = 3ZY.
Simplifying, we get 5 = 4ZY.
Dividing both sides by 4, we get ZY = 5/4.
Therefore, the length of YZ is 5/4.
Let's call the point of intersection between XY and BC as Z.
Since AX/XB = 3/4, we can say that AZ/ZB = 3/4. Similarly, we can say that AY/YC = 5/5 = 1.
Now, let's consider triangles AZX and CZY.
Since the corresponding sides of these triangles are proportional (AZ/ZC = 3/1 and AX/XY = 3/3 = 1), we can conclude that these triangles are similar.
Using the concept of similar triangles, we know that the ratio of the lengths of corresponding sides is the same.
Therefore, we can say that AZ/ZY = 3/1.
Now, we know that AY = 5, so AZ = AY - ZY = 5 - ZY.
Substituting this value in the equation AZ/ZY = 3/1, we get (5 - ZY)/ZY = 3/1.
Cross-multiplying, we get 5 - ZY = 3ZY.
Simplifying, we get 5 = 4ZY.
Dividing both sides by 4, we get ZY = 5/4.
Therefore, the length of YZ is 5/4.
Community Answer
In triangle ABC, if x and y are points on AB and AC respectively such ...
XY cannot be parallel to XB no possible at all
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In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not
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In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not .
In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC, if x and y are points on AB and AC respectively such that AX/XB=3/4 ,AY=5 & YC=9 THEN state weather XY and XB are parallel or not .
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