Student can formally distinguish between non-intersecting lines, secants, and tangents, and define the point of contact.
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Visual recreation of Fig. 10.1 showing non-intersecting, secant, and tangent.
Clean side-by-side comparison, consistent visual treatment for both sides, same scale and style, pastel color coding to …
Defines the three possibilities for a line and a circle in a plane.
When a straight line meets a circle in a plane, there are distinct positional possibilities based on their intersections.
Highlights Activity 1 conclusion that a tangent is a special case of a secant.
The tangent to a circle is actually a special case of the secant. It occurs exactly when the two end points of the secant's corresponding chord merge and coincide into a single point!
Defines point of contact and maximum parallel tangents.
The unique point where the tangent and the circle meet is called the point of contact. We say the tangent touches the circle exactly at this single point, rather than cutting through it.
Fill in the blanks from Exercise 10.1 Q2.
Let us review the fundamental properties of lines and circles based on intersections. A tangent to a circle intersects it in exactly point. In contrast, a line intersecting a circle in two distinct points is called a . When considering parallel lines across the shape, a circle can have parallel tangents at the most. Finally, the exact common point shared by a tangent and the circle is formally called the .