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

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**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 the**point 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.

### Secant

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:

*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.

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### Common Internal and External Tangents: recognize Lengths

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

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