JEE Exam > JEE Questions > in an acute angled triangle ABC, AP is the al...
Start Learning for Free
in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to
Most Upvoted Answer
in an acute angled triangle ABC, AP is the altitude. Circle drawn with...
Proof that the length of DE in an acute angled triangle ABC is equal to AP
Introduction
In an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively. In this proof, we will show that the length DE is equal to AP.
Proof
- Let O be the center of the circle with AP as its diameter.
- Since AP is the diameter, angle AOD and angle AOE are both 90 degrees (as they are angles in a semi-circle).
- Therefore, quadrilateral AODE is a cyclic quadrilateral (as opposite angles add up to 180 degrees).
- By the cyclic quadrilateral theorem, angle ADE is equal to angle AOE.
- Similarly, angle AED is equal to angle AOD.
- Since angles AOE and AOD are both 90 degrees, angles ADE and AED are equal.
- Therefore, triangle ADE is an isosceles triangle.
- Thus, DE is equal to AD (as opposite sides in an isosceles triangle are equal).
- But AD is equal to AP (as AP is the altitude of triangle ABC).
- Therefore, DE is equal to AP.
Conclusion
In an acute angled triangle ABC, if AP is the altitude and a circle is drawn with AP as its diameter that cuts the sides AB and AC at D and E respectively, then the length DE is equal to AP.
Community Answer
in an acute angled triangle ABC, AP is the altitude. Circle drawn with...
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to
Question Description
in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to.
in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to.
Solutions for in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to defined & explained in the simplest way possible. Besides giving the explanation of
in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to, a detailed solution for in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to has been provided alongside types of in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to theory, EduRev gives you an
ample number of questions to practice in an acute angled triangle ABC, AP is the altitude. Circle drawn with AP as its diameter cuts the sides AB and AC at D and E respectively, the length DE is equal to tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup