Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define inscribed and circumscribed circles.
• Identify the center and radius of these circles.
• Draw inscribed and circumscribed circles for triangles.
• Calculate the radius of an inscribed circle.

Lesson summary

This lesson introduces learners to two important geometric constructions: the inscribed circle (incircle) and the circumscribed circle (circumcircle) of a triangle. Understanding these constructions is not just an exercise in drawing; it builds a foundation for more advanced geometry and has practical applications in design, architecture, and engineering. In our Ghanaian context, the principles of geometric harmony are seen in Adinkra symbols, Kente patterns, and even in how community spaces are planned. This lesson will equip learners with the precision skills to find the unique "centers" of a triangle and draw circles that fit perfectly inside or around it.

Lesson notes

A. Introduction: The Two Special Circles of a Triangle

Every triangle has two special circles associated with it: one that fits perfectly inside and one that passes perfectly around its corners. Inscribed Circle (or Incircle): This is the largest possible circle that can be drawn *inside* a triangle. It touches all three sides of thetriangle at a single point each. Circumscribed Circle (or Circumcircle): This is a circle that passes through all three *vertices* (corners) of a triangle. The triangle is completely inside this circle.

To draw these circles, we first need to find their centers. These centers have special names: the Incenter and the Circumcenter.

B. Constructing the Inscribed Circle (Incircle)