Question
In a triangle ABC, D, E and F are the mid-points of the
sides BD, CA and AB, respectively. BE and DF intersect at X. DE and CF intersect at Y. Find XY = ?Solution
In ΔABC, F is the midpoint of AB and E is the midpoint of AC. ∴ By Midpoint Theorem, EF ∥ BC ∴ EF ∥ BD ----(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
Consider the following statements about the Preamble:
1. The Preamble has been amended only once so far under the Prime Ministership of Mrs. Indi...
The biggest consumer of Uranium in the World is:
Where is the World Economic Forum headquartered?
Which of the following services is provided to PMJDY account holders at zero cost?
Which of the following Statements about the National Council for Vocational Education and Training (NCVET) is/are True?
I- It comes under the Min...
ICICI Bank was constituted as first Universal Bank in India
With which act social security was introduced in India?
Recently Coast Guards of India and their Japanese counterpart conducted joint naval exercise near:
On which date International Day of Neutrality is celebrated annually?
RBI is regulator and supervisor of
Relevant for Exams:
