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Scientific Notation Length Conversion Area Conversion

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Power of a Point Theorem

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The Chord Theorem
The Tangent-Secant Theorem
The Intersecting Secants Theorem
AE · CE = DE · BE
AE
CE
DE
BE

Knowledge

In elementary plane geometry, the power of a point is a real number h that reflects the relative distance of a given point from a given circle.

AE · CE = DE · BE
BA2 = BC · BD
CB · CA = CD · CE

Example 1

Find the value of x in the following diagram:

AB · AC = AD · AE

3 · (3+5) = x(x+10)

x2 + 10x - 24 = 0

(x+12)(x-2) = 0

x = 2

Example 2

Find the value of x in the following diagram:

EA · DA = CA · BA

6 · x = 4 · 1

x = 23

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Please provide numbers only. Please provide at least two numbers. Please provide 2 to 10 non-zero integer numbers. None