Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Live 1-1 coding classes to unleash the creator in your Child
Prove that the sum of the distances of any point within a triangle , from its vertices , is less than the perimeter of the triangle .
Dear Abhinav Sharma, consider an equlateral triangle abc,
Dear Abhinav Sharma,
consider an equlateral triangle abc,
Let us draw lines DE parallel to AC, FG parallel to AB, IJ parallel to BC. Triangles FPJ, DIP, and PGE are similar to ABC and therefore are equilateral.
Denote the heights of the triangles FPJ, DIP, PGE, and ABC by e, f, g, h, respectively. e/h = FJ/AC, f/h = DI/AB, g/h = GE/BC. Let us add these thee equalities. Note that DP = AF and PE = JC because ADPF and JPEC are parallelograms. Using the fact that three sides of each of FPJ, DIP, PGE, and ABC are equal, we get the following equality: (e+f+g))/h = 1.
We are all IITians and here to help you in your IIT JEE preparation.
Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..
AMAN BANSAL
But you didnt answer my question , I asked to prove the following :Prove that : AP + PC + PB < AB + BC + AC . ( Point lying anywhere within a triangle ).
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -