How to Construct the Incircle of a Triangle
- Straightedge or Ruler: For creating straight lines and measurements.
- Compass: Indispensable for constructing arcs and circles.
- Pencil: For marking and drawing.
Examples
Practice Questions:
- Can an obtuse triangle have an incircle that touches all its sides? Explain.
- Given an equilateral triangle of side length \(9 \text{ cm}\), how would you find its inradius without constructing the incircle?
- Does the incenter of a triangle always lie within the triangle?
- Yes, every triangle, including obtuse triangles, has a unique incircle that touches all its sides.
- For an equilateral triangle with side length \(a\), the inradius \(r\) can be found using the formula:
\( r = \frac{a}{2\sqrt{3}} \)
For \(a = 9 \text{ cm}\), \(r = \frac{9}{2\sqrt{3}} = \frac{9\sqrt{3}}{6} = 1.5\sqrt{3} \text{ cm}\). - Yes, the incenter always lies inside the triangle.
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