Construction of incircle of a triangle — lesson. Mathematics State Board, Class 9.

PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo

Incentre: It is the point of concurrency of a triangle formed by the intersection of its three angle bisectors of a triangle. It is denoted by

$I$ .

Incircle:It is the circle drawn inside the triangle with incentre as its centre.

Working rule to construct the Incircle of a Triangle

Case 1:

Given the length of two sides of a triangle and the measure of one of its interior angle.

Example:

Construct the incircle of a triangle

$ABC$ given

$AB = 8$

$cm$ ,

$BC = 6$

$cm$ and

$\angle BAC = 55^{\circ}$ . Locate its incentre and find the radius.

Construction:

Step 1: Draw a rough figure for the given question to get the picture of the triangle that is to be constructed.

Step 2: Draw a line segment

$AB = 8$

$cm$ using the ruler.

Step 3: With

$A$ as centre, mark an angle

$55^{\circ}$ using the protractor and name it as

$X$ . Now join

$AX$ .

Step 4: With

$B$ as centre, measure

$6$

$cm$ in the compass and cut an arc intersecting

$AX$ and mark it as

$C$ .

Step 5: Draw the angle bisectors of any two angles of the triangle

$A$ and

$B$ (say).

Step 6: Mark the intersecting point of the angle bisectors as

$I$ , which is the incentre of the given triangle.

Step 7: Draw a perpendicular bisector from

$I$ to one of the sides of the triangle

$AB$ (say) to meet

$AB$ at

$D$ .

Step 8: Measure the length of

$ID$ to get the inradius of the incircle.

Step 9: With

$I$ as centre and

$ID$ as radius, draw the incircle of the triangle.

Case 2:

Given the length of a side of a triangle and the measure of two of its interior angle.

Example:

Construct the incircle of a triangle

$ABC$ given

$AB = 6$

$cm$ ,

$\angle BAC = 55^{\circ}$ and

$\angle CBA = 60^{\circ}$ . Locate its incentre and find the radius.

Construction:

Step 1: Draw a rough figure for the given question to get the picture of the triangle that is to be constructed.

Step 2: Draw a line segment

$AB = 6$

$cm$ using the ruler.

Step 3: With

$A$ as centre, mark an angle

$55^{\circ}$ using the protractor and name it as

$X$ . Now join

$AX$ .

Step 4: With

$B$ as centre, mark an angle

$60^{\circ}$ using the protractor and name it as

$Y$ . Now join

$BY$ .

Step 5: Mark the intersecting point of

$AX$ and

$BY$ as

$C$ .

Step 6: Draw the angle bisectors of any two angles of the triangle

$A$ and

$B$ (say).

Step 7: Mark the intersecting point of the angle bisectors as

$I$ , which is the incentre of the given triangle.

Step 8: Draw a perpendicular bisector from

$I$ to one of the sides of the triangle

$AB$ (say) to meet

$AB$ at

$D$ .

Step 9: Measure the length of

$ID$ to get the inradius of the incircle.

Step 10: With

$I$ as centre and

$ID$ as radius draw the incircle of the triangle.

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

11. Construction of incircle of a triangle

Theory: