Question
Download Solution PDFIn a ΔABC, D, E and F are the mid-points of the sides BC, CA and AB, respectively. BE and DF intersect at X. DE and CF intersect at Y. Find XY.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFIn ΔABC,
F is the midpoint of AB and E is the midpoint of AC.
∴ By Midpoint Theorem,
EF ∥ BC
∴ EF ∥ BC ----(1)
⇒ EF = BC/2 ----(2)
Since D is the midpoint of BC,
⇒ EF = BD ----(3)
From equation 1 and 3,
⇒ BDEF is a Parallelogram.
BE and DF intersect at X.
Similarly, DCEF is a Parallelogram.
DE and CF intersect at Y.
∵ X and Y are the midpoints of sides DF and DE, respectively.
In ΔDEF,
X is the midpoint of DF and Y is the midpoint of DE.
∴ By Midpoint Theorem,
⇒ XY = EF/2 ----(4)
From equation 3 and 4
⇒ XY = BC/4
Last updated on Jun 2, 2025
-> The RRB NTPC Admit Card 2025 has been released on 1st June 2025 on the official website.
-> The RRB Group D Exam Date will be soon announce on the official website. Candidates can check it through here about the exam schedule, admit card, shift timings, exam patten and many more.
-> A total of 1,08,22,423 applications have been received for the RRB Group D Exam 2025.
-> The RRB Group D Recruitment 2025 Notification was released for 32438 vacancies of various level 1 posts like Assistant Pointsman, Track Maintainer (Grade-IV), Assistant, S&T, etc.
-> The minimum educational qualification for RRB Group D Recruitment (Level-1 posts) has been updated to have at least a 10th pass, ITI, or an equivalent qualification, or a National Apprenticeship Certificate (NAC) granted by the NCVT.
-> This is an excellent opportunity for 10th-pass candidates with ITI qualifications as they are eligible for these posts.
-> The selection of the candidates is based on the CBT, Physical Test, and Document Verification.
-> Prepare for the exam with RRB Group D Previous Year Papers.