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Student can state the number of tangents from points relative to the circle and prove/apply Theorem 10.2 (Lengths of external tangents are equal).
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Summarizes the three cases based on the location of a point relative to a circle.
A crucial property of tangents is how their existence depends entirely on the location of a point relative to the circle. We can break this down into three distinct scenarios.
Reproduces Figure 10.6 (i, ii, iii) showing the number of tangents.
clean side-by-side comparison, consistent visual treatment for both sides, same scale and style, pastel color coding to …
Statement and RHS proof of Theorem 10.2.
The lengths of tangents drawn from an external point to a circle are equal.
When you draw two tangents from a single point outside the circle, the distance from that point to the respective points of contact will always be exactly the same.
Reproduces Figure 10.7 for the proof of Theorem 10.2.
Clean scientific diagram of a geometric figure. A circle with center point O. An external point P lies outside to the le…
Formalizes the equality and the angle bisector property.
The lengths of two tangents drawn from an external point to a circle are exactly equal.
The center of the circle lies exactly on the bisector of the angle between the two tangents.
A basic application of the theorem.
If and are two tangents to a circle from an external point , and the length of is , what is the length of ?