Math 10 - 3rd periodical exam

Circles

Are geometric figures that you see all around. It is the set of al points that are of the same distance from a given point in a plane

Center

What do you call the given point of the circle?

Radius

A line from the center of a circle to a point from the circumference of a circle

Radii

It is composed of two radius

Chord

A segment whose endpoints lie on the circle

Diameter

It is a chord that passes through the center of the circle

Interior of the circle

The set of points in the plane of a circle whose distances from the center are less than the length of the radius

Exterior of the circle

The set of points in the plane of a circle whose distances from the center are greater than the length of the radius

Tangent

A line which touches the circle at only one point. It does not cross the circle

Point of tangency

The point of contact of the circle and the tangent line

Secant

The line that intersects a circle at two points

Arc

The part or segment of the circumference of a circle. It has different types

Semicircle

an arc of a circle whose endpoints are the endpoints of a diameter

Minor arc

An arc of a circle that is less than a semicircle

Major arc

An arc of a circle that is greater than a semicircle

Central angle

Angles whose common vertex is the center of the circle and whose sides are the radii of the circle

Congruent arcs

In the same circle or arcs that have the same measures

Inscribed angles

Angles whose vertices are points of the circle

Theorem 1.1

Congruent chords of a circle are equidistant from the center of the circle

theorem 1.2

The measure of an inscribe angle in a circle is half the measure of the arc it intercepts

Theorem 1.3

In a circle, inscribed angles that intercepts the same arc or congruent arcs are congruent

Theorem 1.4

In a circle, an inscribed angle that intercepts a semicircle is a right angle

Theorem 1.5

Opposite angles of a quadrilateral inscribed in a circle are supplementary