How to Construct the Incircle of a Triangle

The incircle of a triangle is the largest circle that fits inside it, touching all three sides. Its center is the incenter, found where the three angle bisectors meet.

• Straightedge or Ruler: For creating straight lines and measurements.
• Compass: Indispensable for constructing arcs and circles.
• Pencil: For marking and drawing.

Worked examples: constructing the incircle

Practice questions on the incircle of a triangle

1. Can an obtuse triangle have an incircle that touches all its sides? Explain.
2. Given an equilateral triangle of side length (9 text{ cm}), how would you find its inradius without constructing the incircle?
3. Does the incenter of a triangle always lie within the triangle?

1. Yes, every triangle, including obtuse triangles, has a unique incircle that touches all its sides.
2. For an equilateral triangle with side length (a), the inradius (r) can be found using the formula:
   ( r = frac{a}{2sqrt{3}} )
   For (a = 9 text{ cm}), (r = frac{9}{2sqrt{3}} = frac{9sqrt{3}}{6} = 1.5sqrt{3} text{ cm}).
3. Yes, the incenter always lies inside the triangle.

The Ultimate Algebra Bundle 2026 From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

The Ultimate Elementary School Math Bundle Grade 3-5

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.