# Inequalities In A Triangle Free Doubts and Solutions

### CBSE - IX - Mathematics - Triangles

## What is the greatest possible perimeter of a right angeled triangle with integer sides lengths if one of the sides has length 12?

**vikasg13.hardware**13th June 2018, 12:01 PM

### CBSE - IX - Mathematics - Triangles

## Solve question no. 75

**vikasg13.hardware**29th December 2017, 11:38 AM

### CBSE - IX - Mathematics - Triangles

## Please solve question no. 60

**vikasg13.hardware**29th December 2017, 11:28 AM

### CBSE - IX - Mathematics - Triangles

## ABC is a triangle in which *L*B=2*L*C. D is a point on BC such that AD bisects *L*BAC and AB=CD. Prove that *L*BAC=72 degree.

*L*B=2

*L*C. D is a point on BC such that AD bisects

*L*BAC and AB=CD. Prove that

*L*BAC=72 degree.

**aahnik.mohanty**21st December 2017, 9:22 PM

### CBSE - IX - Mathematics - Triangles

## In a right angled triangle, one acute angle is double the other. Then the hypotenuse is 'k'times the smallest side. The k=?

**aahnik.mohanty**26th November 2017, 8:30 PM

### CBSE - IX - Mathematics - Triangles

## Prove that the sum of the three altitudes of a triangle is less than the sum of the three sides of the triangle.

**Topperlearning User**11th August 2017, 10:06 AM

### CBSE - IX - Mathematics - Triangles

## In the figure AD is the bisector of A, prove that AB > BD.

**Topperlearning User**11th August 2017, 10:04 AM

### CBSE - IX - Mathematics - Triangles

## Show that of all line segment drawn from a given point not on it, the perpendicular line segment is the shortest.

**Topperlearning User**11th August 2017, 9:55 AM

### CBSE - IX - Mathematics - Triangles

## There is a triangular field ABC whose corner angles A, B and C have been measured as 50o, 60o and 70o respectively. Three friends Rashmi, Salma and Arun daily go on morning walk and respectively walk along AB, BC and AC. Who walks maximum distance among these three? Who walks the least? What value is indicated from this action?

**Topperlearning User**11th August 2017, 9:50 AM

### CBSE - IX - Mathematics - Triangles

## In fig., if a > b then prove that PQ > PR.

**Topperlearning User**11th August 2017, 9:23 AM

### CBSE - IX - Mathematics - Triangles

## In a ΔDEF, if D = 30° E = 60° then which side of the triangle is longest and which side is shortest?

**Topperlearning User**11th August 2017, 9:22 AM

### CBSE - IX - Mathematics - Triangles

## In fig., D is any point on the base BC produced of an isosceles triangle ABC. Prove that AD > AB.

**Topperlearning User**11th August 2017, 9:22 AM

### CBSE - IX - Mathematics - Triangles

## In the given figure, ABD = 130° and EAC = 120°. Prove that AB > AC.

**Topperlearning User**11th August 2017, 9:21 AM

### CBSE - IX - Mathematics - Triangles

## In figure , AB > AC, BO and CO are the bisectors of B and C respectively. Show that OB > OC.

**Topperlearning User**11th August 2017, 9:21 AM

### CBSE - IX - Mathematics - Triangles

## In fig., PR > PQ and PS bisects QPR. Prove that PSR > PSQ.

**Topperlearning User**11th August 2017, 9:19 AM

### CBSE - IX - Mathematics - Triangles

## Show that in a right angled triangle the hypotenuse is the longest side.

**Topperlearning User**11th August 2017, 9:18 AM

### CBSE - IX - Mathematics - Triangles

## In figure, D is a point on side BC of such that AD=AC. Show AB>AD.

**Topperlearning User**11th August 2017, 9:18 AM

### CBSE - IX - Mathematics - Triangles

## Prove that the sum of any two sides of a triangle is greater than twice the length of median drawn to the third side.

**Topperlearning User**11th August 2017, 9:14 AM

### CBSE - IX - Mathematics - Triangles

## In figure, show that 2 (AC + BD) > (AB + BC + CD + DA)

**Topperlearning User**11th August 2017, 9:13 AM

### CBSE - IX - Mathematics - Triangles

## The side BC of ABC is produced on both sides. Prove that the sum of the two exterior angles so formed is greater than A by 180o.

**Topperlearning User**11th August 2017, 9:11 AM

### CBSE - IX - Mathematics - Triangles

## If AD is the bisector of A of ABC, show that AB > DB.

**Topperlearning User**11th August 2017, 9:10 AM

### CBSE - IX - Mathematics - Triangles

## In figure, AB and CD are respectively the smallest and the longest sides of a quadrilateral ABCD, then show that A > C and B > D.

**Topperlearning User**11th August 2017, 9:09 AM

### CBSE - IX - Mathematics - Triangles

## In triangle ABC, D is a point on AC, Prove that, the value of the perimeter of triangle ABC is greater than twice the length of BD.

**Topperlearning User**11th August 2017, 9:07 AM

### CBSE - IX - Mathematics - Triangles

## Prove that diagonals of a rectangle are equal but not perpendicular.

**Topperlearning User**11th August 2017, 9:07 AM

### CBSE - IX - Mathematics - Triangles

## The sides of AB, BC, AC a triangle ABC are 2.8 cm, 3.7 cm and 4.1 cm respectively. What is the relationship between the angles A, B, and C?

**Topperlearning User**11th August 2017, 9:04 AM

### CBSE - IX - Mathematics - Triangles

## Prove that if the median AD of a triangle ABC is greater than half of BC, then,

**Topperlearning User**11th August 2017, 9:03 AM

### CBSE - IX - Mathematics - Triangles

## In triangle ABC, AB = BC; angle B is half of angle A. Is AB > AC? Give reason for your answer.

**Topperlearning User**11th August 2017, 8:51 AM

### CBSE - IX - Mathematics - Triangles

## In a triangle ABC, AB = 3 cm, BC = 3.5 cm and CA = 6.5 cm. Is it possible to construct this triangle? Give reason for your answer.

**Topperlearning User**11th August 2017, 8:48 AM

### CBSE - IX - Mathematics - Triangles

## Prove that in a right triangle, the hypotenuse is the longest side.

**Topperlearning User**11th August 2017, 8:48 AM

### CBSE - IX - Mathematics - Triangles

## In the figure PQ > PR, QS and RS are the bisectors of Q and R respectively. Prove that SQ > SR.

**Topperlearning User**11th August 2017, 8:47 AM

### CBSE - IX - Mathematics - Triangles

## Prove that if two sides of a triangle are unequal, the longer side has greater angle opposite it.

**Topperlearning User**11th August 2017, 8:47 AM

### CBSE - IX - Mathematics - Triangles

## Prove that the perimeter of a triangle is greater than the sum of its three medians.

**Topperlearning User**11th August 2017, 8:45 AM

### CBSE - IX - Mathematics - Triangles

## In the given figure, x > y. Show that LM > LN.

**Topperlearning User**11th August 2017, 8:40 AM

### CBSE - IX - Mathematics - Triangles

## Can you give me some difficult prove that questions with its solution ?

**gpnkumar0**13th September 2016, 8:48 AM

### CBSE - IX - Mathematics - Triangles

## Show that the sum of the three altitudes of a triangle is less than the sum of three sides of the triangle.

**gpnkumar0**12th September 2016, 3:27 PM

### CBSE - IX - Mathematics - Triangles

**In a triangle, prove that the greater angle has the longer side opposite to it**

**In a triangle, prove that the greater angle has the longer side opposite to it**

**gpnkumar0**5th September 2016, 8:53 PM

### CBSE - IX - Mathematics - Triangles

In a right angled triangle, one acute angle is double the other. Then the hypotenuse is _______.

(A) Double the smallest side

(B) Thrice the smallest side

(C) 4 times the smallest side

(D) None

**gpnkumar0**5th August 2016, 6:31 PM

### CBSE - IX - Mathematics - Triangles

##
**O** is any point in the interior of a triangle **ABC** then **AB + AC** is _________.

**O** is any point in the interior of a triangle **ABC** then **AB + AC** is _________.

**gpnkumar0**5th August 2016, 6:24 PM

### CBSE - IX - Mathematics - Triangles

In triangle **ABC**, **AD **is the median. Then **AB + AC **is _________.

**ABC**,

**AD**is the median. Then

**AB + AC**is _________.

**gpnkumar0**5th August 2016, 6:18 PM

### CBSE - IX - Mathematics - Triangles

## <div>If I is the incentre of<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=6652abdbffb74104943625e3253daf18.png" alt="increment A B C" align="middle" /> and AI is produced to meet BC at X , then AI :IX = ?</div>

**Alok**31st March 2016, 8:53 PM

### CBSE - IX - Mathematics - Triangles

##
P, Q and R are respectively , the midpoints of sides BC, CA and AB of a triangle ABC. PR and BQ meets X. CR and PQ meet at Y. Prove that XY = 1/4 BC

P, Q and R are respectively , the midpoints of sides BC, CA and AB of a triangle ABC. PR and BQ meets X. CR and PQ meet at Y. Prove that XY = 1/4 BC

**Paresh**11th December 2015, 2:36 PM

### CBSE - IX - Mathematics - Triangles

## If sin A + sin B + sin C = 3, find cos A + cos B + cos C.

**a.behera67**20th October 2015, 2:40 PM

### CBSE - IX - Mathematics - Triangles

## In triangle ABC , I is the incentre. If angles BIC:CIA:AIB = 5 : 6 : 7 ,Then the value of angles A : B: C is:

**Kusum and Sanjeet**11th November 2014, 8:08 PM

### CBSE - IX - Mathematics - Triangles

## if AB=CB, AB=CD, and EF bisects BD at G .prove that G is mid point of EF.

**vaibhavmishratempleton**22nd August 2014, 11:25 PM