OBJECTIVE - G.C.A.4

Construct a tangent line from a point outside a given circle to the circle.

INTERPRETATION OF OBJECTIVE - G.C.A.4

No interpretation needed here.

SKILLS

(1) The student will be able to construct the tangent line to a circle through a given exterior point.

THE BIG IDEA

Circle constructions provide a way to connect circle properties to the physical construction. One of the themes of the entire curriculum in the inclusion of constructions as a way to visual and connect concepts.

TRAPS & PITFALLS

This is a honors construction for a reason. The breakthrough idea is not very apparent. It isn't a hard construction to perform - it is just hard to come up with the steps on your own. I like to troubleshoot this one using groups.

PAST CONNECTIONS

Throughout the entire year constructions are used to connect concepts in a visual way. Constructions are a physical way to demonstrating understanding.

FUTURE CONNECTIONS

Building confidence with constructions provide ways for students to work out future problems. The construction tools of straightedge and compass provide additional tools to solving geometry related problems.

MY REFLECTIONS (over line l)

I like to leave this problem wide open and then have students work together to try and solve it. It is within reach of high school students but it is a 'hidden' idea. If nothing is happening then I begin giving small hints. I talk about ways to created right angles, what circle properties deal with right angles, etc...