Here we comment on the assorted symmetry and also angle nature of tangents come circles.

You are watching: What does the radius-tangent theorem state?

Related Pages Tangents that Circles and also Angles angles In A Circle one Cyclic quadrilateral

In this lessons us will learn about

Tangent to A Circle and The point Of Tangency,Tangent come A circle Theorem,Secant,Two-Tangent Theorem,Common Internal and External Tangents.

The complying with diagrams present the Radius Tangent Theorem and also the Two-Tangent Theorem. Scroll down the page for an ext examples and solutions.


Tangent to A Circle

A tangent come a one is a directly line, in the plane ofthe circle, which touches the one at just one point. The allude is dubbed thepoint the tangency or the pointof contact.

Tangent to a one Theorem: A tangent to a circleis perpendicular come the radius attracted to the point of tangency.


What Is The Tangent of A Circle?

A tangent is a heat in the airplane of a circle the intersects the circle in ~ one point.The allude where that intersects is called the point of tangency.

How to Prove The Tangent to A one Theorem?

The Tangent come a circle Theorem claims that a line is tangent to a circle if and only if theline is perpendicular to the radius drawn to the allude of tangency.


A right line that cut the circle in ~ two unique points is referred to as a secant.


Example:In the following diagram a) state every the tangents come the circle and the point of tangency of every tangent. B) state every the secants.


Solution:AB is a tangent come the circle and the suggest of tangency is G.CD is a secant come the circle because it has actually two clues of contact. EF is a tangent to the circle and also the point of tangency is H.

Tangents native The Same outside Point

Two-Tangent Theorem: when two segments are attracted tangent toa circle indigenous the same allude outside the circle, the segments are equal in length.

In the adhering to diagram: If AB and AC space two tangents come a circle centered at O, then:

the tangents come the circle native the external suggest A are equal,OA bisects the angle BAC between the two tangents,OA bisects the angle BOC between the 2 radii to the clues of contact,triangle AOB and also triangle AOC are congruent ideal triangles.

The two-tangent theorem is likewise called the "hat" or "ice-cream cone" theorembecause that looks like a hat on the one or an ice-cream cone.

How to Prove The Two-Tangent Theorem?

The Two-Tangent Theorem claims that when two segment are drawn tangent to a circle indigenous thesame point outside the circle, the segments room congruent. (uses Two-Column Proof and also CPCTC).

When 2 Tangent currently Emanate native The Same exterior Point

How to uncover an unknown angle utilizing the two-tangent theorem?

How To use The Two-Tangent organize To settle A Geometry Problem?

How To apply The Congruent Tangents organize Or Two-Tangent Theorem?

Common Internal and External Tangents

A usual tangent is a line that is a tangent to each of 2 circles. A usual external tangent does not intersect the segment the joins the centers of the circles. A typical internal tangent intersects the segment that joins the centers of the circles.

See more: The Largest High School Football Game Attendance ? Eagle Stadium (Allen, Texas)

Common Internal and External Tangents: recognize Lengths

A lesson on detect the length of common internal and also external tangents.

Try the complimentary Mathway calculator and problem solver below to practice assorted math topics. Try the given examples, or kind in your own problem and also check her answer v the step-by-step explanations.