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# Circle (Geometry)

See how to solve circle problems
(arc/segments/angles/area).
25 examples and their solutions.

C = 2πr

C = πd

Circumference?

Solution

Circumference?

Solution

mAB = θ

mAB = ?

Solution

Length of AB = ?

Solution

## Chord of a Circle

### Definition

A chord is a line segment
whose endpoints are on the circle.

### Property

A line segment that passes through the center
perpendicularly bisects the chord.

AB = ?

Solution

## Inscribed Angle

### Formula

θ = 12mAB
θ: Inscribed angle
mAB: Intercepted arc

Solution

mABC = ?

Solution

Solution

## Inscribed Right Triangle

### Property

The hypotenuse of an inscribed right triangle
passes through the center of the circle.

Solution

Solution

### Property

m∠1 + m∠2 = 180
m∠1' + m∠2' = 180
The opposite angles are supplementary angles.

Solution

## Tangent to a Circle

### Definition

A tangent to a circle is a line
that touches the circle.
From a point exterior of the circle,
you can draw two tangents.

### Property

are perpendicular
at the intersecting point of the circle.

PB = ?

Solution

### Example

Perimeter of △ABC?

Solution

θ = 12mAB

mAB = 110, x = ?

Solution

Solution

## Angle Formed by Two Chords

### Formula

θ = 12(mAC + mBD)

Solution

## Angle Formed by Two Secants

### Formula

θ = 12(mBD - mAC)

Solution

## Angle Formed by a Tangent and a Secant

### Formula

θ = 12(mBC - mAC)

Solution

## Angle Formed by Two Tangents

### Formula

θ = 12(mABC - mAC)

Solution

APPB = CPPD

Solution

PAPB = PCPD

Solution

PA2 = PBPC

Solution

A = πr2

Area?

Solution

Area?

Solution

Area?

Solution