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In ABC, the angle bisectors meet at point D. Point E is on AC, DE and is perpendicular to AC . Point F is the location where the perpendicular bisectors of the sides of the triangle meet. What is the radius of the largest circle that can fit inside ABC?

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caylus
Hello,

Radius of the inscribed circle is |DE|


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Answer with explanation:

β†’It is given that in Ξ”ABC,the angle bisector of each angle of triangle ABC meet at point D.

β†’To draw the in circle draw perpendicular from point D on any of three sides of triangle,and then suppose it cuts the triangle at X,Y and Z . Taking any of D X,DY and DZ as a radius we can draw the in circle of given triangle.

β†’In-center of a triangle is that point inside a triangle where internal bisector of triangle meet.

Also, it is given that, DEβŠ₯AC.

β†’Line from center of a circle to the point of contact of a line called tangent,are perpendicular to each other.

So,β†’ Radius of largest circle that can fit inside Ξ”ABC= DE

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