Q2 of 17 Page 175

Draw incircle of an equilateral triangle of side 4.6 cm. Do its circumcentre and incentre coincide with each other? Give reason for your answer

Steps of Construction:


1. Draw an equilateral triangle of side 4.6cm



2. Draw angle bisector of ∠A.



3. Draw angle bisector of ∠B.



4. They intersect each other at P.


5. From P, drop a perpendicular on the line AB.



6. With P as center and length of perpendicular as the radius, draw a circle.



This circle is the incircle for the equilateral triangle.


Yes. The incenter and circumcenter of the equilateral triangle coincide with each other. This is because the perpendicular dropped from P on AP is also the perpendicular bisector of AB.


More from this chapter

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11

The radii of two circles are 1.7 cm and 2.8 cm, and their centers are 6 cm apart. Construct a transverse common tangent to the two circles.

 1

Write the truth value (T/F) of each of the following statements. If possible, give reason for your answer.

(i) In an equilateral triangle, the incircle and the circumcircle can be constructed with the same centre.


(ii) The incircle of a triangle touches all sides of the triangle.


(iii) In an obtuse-angled triangle, the circumcenter lies on one of the sides of the triangle.


(iv) In an acute-angled triangle, the circumcentre lies inside the triangle.


(v) The incircle of a triangle is constructed by locating the point of intersection of perpendicular bisectors of any two sides of the triangle.

 3

Draw incircle of a triangle ABC where AB = 4.6 cm, AC = 4.2 cm and ∠A = 90°.

 4

Draw circumcircle of a triangle whose sides are 10.5 cm, 12.7 cm and 13 cm respectively. Also give reason as to why its circumcentre is located on the side of length 13 cm.