# Centre of Triangle in Geometry, Study Notes, Material - CTET Paper 1& 2

By Neha Joshi|Updated : June 11th, 2021

In this Article we should study, Centre of Triangle in Geometry, Important for the CTET.

इन-सेंटर-एक ट्रायंगल के सभी तीनों एंगल (कोण) बैसेक्टर्स के मिलने के बिंदु को इन-सेंटर कहा जाता है(In-centre)

• सरकम-सेंटर (Circumcentre)
• सेंट्रोइड (Centroid)
• ऑर्थो सेंटर (Orthocentre)

Centre of Triangle in Geometry

• In-centre:

The point of intersection of all the three angle bisectors of a triangle is called as In-centre

The distance of the in-centre from the all the three sides is equal(ID=IE=IF=inradius “r”)

∠BIC = 90 +∠A/2

∠AIC=90+∠B/2

∠AIB=90+∠C/2

### Circumcentre:

The point of intersection of the perpendicular bisectors of the three sides of a triangle is called its circumcentre.

The distance between the circumcentre and the three vertices of a triangle is always equal.

∠BOC=2∠A

∠AOC=2∠B

∠AOB=2∠C

### Location of circumcentre in various types of triangle:

Acute angle triangle: Lies inside the triangle

Obtuse angle triangle: Lies outside the triangle

Right angle triangle: Lies at the midpoint of the hypotenuse.

### Orthocentre:

It is the point of intersection of all the three altitudes of the triangle.

∠BHC=180-∠A

∠AHB=180-∠C

∠AHC=180-∠B

### Position of orthocentre inside the triangle:

Acute angled triangle: lies inside the triangle.

Obtuse angle triangle: lies outside the triangle on the backside of the obtuse angle. Orthocentre and circumcentre lie opposite to each other in obtuse angle triangle.

Right angle triangle: lies on the right angle of the triangle.

### Centroid:

• It is the point of the intersection of the three median of the triangle. It is denoted by G.
• A centroid divides the area of the triangle in exactly three parts.

### Medians:

• A line segment joining the midpoint of the side with the opposite vertex is called median.
• Median bisects the opposite side as well as divide the area of the triangle in two equal parts.

### Some important tricks are as follows:

(1)In a right angle triangle ABC,∠B=90° & AC is the hypotenuse of the triangle. The perpendicular BD is dropped on the hypotenuse AC from the right angle vertex B,

BD=AB*BC/AC

CD=BC2/AC

1/BD=1/AB2 +1/BC2

(2)The ratio of the areas of the triangles with equal bases is equal to the ratio of their heights.

(3)The ratio of the areas of two triangles is equal to the ratio of products of base and its corresponding sides.

Area (Triangle ABC)/Area (Triangle PQR) =AC*BD/PR*QS

(4)If two triangles have the same base and lie between the same parallel lines then the area of the two triangles will be equal.

Area of Triangle ABC= Area of Triangle ADB

(5)In a triangle ABC, AE, CD  and BF are the medians then

3(AB2+BC2+AC2) = 4(CD2+BF2+AE2)

6)Sum of any two sides of the triangle is always greater than the third sides.

(7)The difference between any two sides of a triangle is always less than the third sides.

This article tends to be beneficial for the following exams - REET, UPTET, CTET, Super TET, DSSSB, KVS, etc.

 Serial No. Book Name Author Name 1. A Complete Resources for CTET: Mathematics and Pedagogy Haneet Gandhi (Pearson) 2. CTET & TETs for Class VI-VII Mathematics & Pedagogy Arihant.

Thanks!

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## FAQs

• The point of intersection of all the three angle bisectors of a triangle is called In-centre.

• The point of intersection of the perpendicular bisectors of the three sides of a triangle is called its circumcentre.

The distance between the circumcentre and the three vertices of a triangle is always equal.

• Orthocentre is the point of intersection of all the three altitudes of the triangle.

•  The weightage of Mathematics Subject in CTET Paper 1 & 2 is 30 marks.

### CTET & State TET Exams

CTETUPTETKVS NVSDSSSBOthers