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**Day eight : The tangent and Secant
line in a circle**

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by Nami Youn

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**Objective**

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To discover the relationship of Tangent line and Secant line of a circle

**Property 1**

**From a point outside a circle,
construct the tangent and secant line.Let the intersection point of the
tangent and the circle be T. Let the intersection points of the secant
and the circle be A and B. Then, PT PT =PAPB**

**If the points A and B lie on
the half line with point P as an endpoint and point T does not lie on this
half line, PT PT =PAPB, then the line PT is a tangent line of this circle
passing through A, B, and T.**

gsp file

**2. Extension**

**Isosceles triangle**

** ABAB =ACAC=APAQ**

gsp file

**The common tangent line of two
circles**

**PAPB = PCPD**

Let the intersection point of extension lines of two chords AB and CD
in a circle be P. If PAPB = PCPD, then the four points A, B, C, and D lie
on a circle.

gsp file

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