Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

Q: If O is the midpoint within increment ABC, show that:
i) AB + AC> OB + OC
ii)AB + BC+CA >OA+OB+OC
iii) OA+OB+OC>1 half(AB + BC + CA)
Asked by kumar.ashlesha | 14 Aug, 2014, 07:50: PM
answered-by-expert Expert Answer
(i)
Consider the following figure.
Produce OB to BD to meet AC at D.
WE know that sum of any two sides of a atriangle is always less than the third side of the triangle.
Thus, we have,
T h u s comma space f r o m space t h e space t r i a n g l e space A B C comma A B plus A C greater than B C... left parenthesis 1 right parenthesis S i m i l a r l y space f r o m space t h e space t r i a n g l e space B C D comma space w e space h a v e B D plus C D greater than B C... left parenthesis 2 right parenthesis T h u s comma space f r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space w e space h a v e A B plus A C greater than B D plus C D... left parenthesis 3 right parenthesis W e space h a v e comma space O B plus O D equals B D... left parenthesis 4 right parenthesis T h u s comma space f r o m space left parenthesis 3 right parenthesis space a n d space left parenthesis 4 right parenthesis comma space w e space h a v e A B plus A C greater than O B plus O D plus C D... left parenthesis 5 right parenthesis B u t space O D plus C D greater than O C... left parenthesis 6 right parenthesis S o comma space f r r o m space left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space h a v e A B plus A C greater than O B plus O C
Answered by Vimala Ramamurthy | 16 Aug, 2014, 11:47: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
questions
question image
Asked by narendrapatidar39877 | 09 Mar, 2024, 11:01: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
mid point theorem
Asked by khshivam2006 | 26 Feb, 2024, 04:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
file
question image
Asked by maheshpatil2067 | 14 Jan, 2024, 04:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
solution
question image
Asked by harshitpal2115 | 30 Dec, 2023, 02:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
if ABCD is a llgm and X and Y are points on the diagonal BD such that DX=BY. Prove that a) AXCY is a llgm
Asked by borakartike2 | 29 Dec, 2023, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
triangle ABC is an equilateral triangle, AB = 6cm. the points P,Q and R are midpoints of AB BC, CA respectively . the perimeter of □ PBCR is
question image
Asked by ghodage | 12 Dec, 2023, 07:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
the area of an equilateral triangle is 49√3 sq.cm, it's perimeter is
Asked by vijaykasaudhan913 | 10 Dec, 2023, 04:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
ABCD is quadrilateral in which P Q R S are mid points of the sides AB BC CD DA. AC is diagonal. show that SR is parallel to AC and SR= 1half 2 AC
Asked by aksharapatni | 30 Nov, 2023, 01:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
in right angle triangle ABC angle B =90 degrees and tanC=1/2.if AC=6cm then then the lenght of side BC is
Asked by rajetigirija | 19 Nov, 2023, 08:11: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
M is a point inside a square ABCD. AMCD is equilateral triangle and MC cuts diagonal DB at E. Then, ZBEC=..... (1) 75° (3) 105° (2) 90° (4) 60°
Asked by Krishna962511 | 23 Jan, 2023, 10:41: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×