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External Point Tangent

An external point tangent refers to a straight line drawn from a point outside a circle that touches the circle at exactly one point. According to geometry principles, exactly two such tangents can be drawn from any single external point to a given circle.

Key Concepts

From any point lying outside a circle, exactly two tangents can be constructed.
The lengths of the two tangents drawn from an external point to the points of contact on the circle are always equal.
The line segment joining the external point to the center of the circle bisects the angle between the two tangents.

Formula & Equation

PT=PQandOP2=OT2+PT2PT = PQ and OP^2 = OT^2 + PT^2

PT and PQ are the lengths of the two tangents from external point P. OP is the distance from the external point to the center O, and OT is the radius of the circle at the point of contact T.

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Common Misconceptions

Myth: Students often think that the two tangents drawn from an external point can have different lengths depending on the angle they are drawn.
Fact: The lengths of both tangents drawn from a single external point to the points of contact on the circle are always strictly equal, as proven by the congruency of the right-angled triangles formed with the circle center.

Real World Applications

The lines of sight of a person looking at the extreme left and right edges of a circular water tank from a distance form two equal tangents.
A V-shaped conveyor belt system where two straight belts touch a circular pulley at exactly two points.

Frequently Asked Questions

How many tangents can be drawn to a circle from an external point?
Exactly two tangents can be drawn to a circle from any given external point.
How do you find the length of a tangent from an external point?
You can find the length using the Pythagoras theorem, where the square of the tangent length equals the square of the distance to the center minus the square of the radius.

Keep Learning

TangentEqual Tangents TheoremExternal Point