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

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Related Pages Tangents that Circles and also Angles angle In A Circle one Cyclic square

In these lessons us will find out about

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

The adhering to diagrams show the Radius Tangent Theorem and also the Two-Tangent Theorem. Scroll under the web page for much more examples and also solutions.

### Tangent come A Circle

A tangent come a one is a directly line, in the airplane ofthe circle, which touch the circle at just one point. The point is referred to as thepoint of tangency or the pointof contact.

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

### What Is The Tangent of A Circle?

A tangent is a heat in the plane of a circle the intersects the circle in ~ one point.The allude where that intersects is referred to as the suggest of tangency.

### How to Prove The Tangent come A one Theorem?

The Tangent to a circle Theorem claims that a heat is tangent come a one if and also only if currently is perpendicular come the radius attracted to the suggest of tangency.

### Secant

A straight line that cut the circle in ~ two distinct points is dubbed a secant.

Example:In the adhering to diagram a) state every the tangents come the circle and also the allude of tangency of each tangent. B) state every the secants.

Solution:AB is a tangent come the circle and also the suggest of tangency is G.CD is a secant come the circle due to the fact that it has two point out of contact. EF is a tangent come the circle and also the allude of tangency is H.

### Tangents indigenous The Same external Point

Two-Tangent Theorem: as soon as two segment are attracted tangent toa circle native the same point outside the circle, the segments space equal in length.

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

the tangents come the circle from the external point A are equal,OA bisects the edge BAC in between the 2 tangents,OA bisects the edge BOC between the two radii come the point out of contact,triangle AOB and also triangle AOC space congruent ideal triangles.

The two-tangent organize is also called the "hat" or "ice-cream cone" theorembecause the looks prefer a hat on the circle or an ice-cream cone.

### How to Prove The Two-Tangent Theorem?

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

### When 2 Tangent currently Emanate native The Same outside Point

How to discover an unknown angle making use of the two-tangent theorem?

### Common Internal and also External Tangents

A typical tangent is a line that is a tangent to each of two circles. A typical external tangent does no intersect the segment that joins the centers the the circles. A common internal tangent intersects the segment the joins the centers the the circles.

See more: " Her Skeleton Will Lie In The Chamber Forever, Her Skeleton Will Lie In The Chamber Forever

### Common Internal and External Tangents: finding Lengths

A great on finding the size of usual internal and external tangents.

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