Geometry - Circles

Question 1

Define Center of a circle

Answer 1

A point inside the circle. All points on the circle are equidistant (same distance) from the center point.

Question 2

What is radius of a circle?

Answer 2

1. A line from the center of a circle to a point on the circle. 2. The distance from the center of a circle to a point on the circle.

Question 3

What is the diameter of a circle?

Answer 3

The distance across a circle through its center point. The diameter of a circle is the length of the line through the center and touching two points on its edge The center of a circle is the midpoint of its diameter. That is, it divides it into two equal parts, each of which is a radius of the circle. The radius is half the diameter.

Question 4

Define circle

Answer 4

A line forming a closed loop, every point on which is a fixed distance from a center point. A circle is a type of line. Imagine a straight line segment that is bent around until its ends join. Then arrange that loop until it is exactly circular - that is, all points along that line are the same distance from a center point. There is a difference between a circle and a disk. A circle is a line, and so, for example, has no area - just as a line has no area. A disk however is a round portion of a plane which has a circular outline. If you draw a circle on paper and cut it out, the round piece is a disk.

Question 5

What is circumference of a circle?

Answer 5

The distance around the edge of a circle. Also ‘periphery’ , ‘perimeter’.

Question 6

What is pi (π)?

Answer 6

Pi is a number - approximately 3.142 It is the circumference of any circle divided by its diameter. The number Pi, denoted by the Greek letter π - pronounced ‘pie’, is one of the most common constants in all of mathematics. It is the circumference of any circle, divided by its diameter. Nobody knows its exact value, because no matter how many digits you calculate it to, the number never ends. For most practical uses, you can assume it is 3.142.

Question 7

Given radius of a circle how do you calculate circumference?

Answer 7

Circumference = 2πr where r is radius Alternatively circumference = πd where d is diameter of the circle.

Question 8

What is the area enclosed by a circle?

Answer 8

The number of square units it takes to exactly fill the interior of a circle. A circle is actually a line, one that connects back to itself making a loop. Imagine the circle to be a loop of string. The string itself has no area, but the space inside the loop does. So strictly speaking a circle has no area. However, when we say “the area of a circle” we really mean the area of the space inside the circle. If you were to cut a circular disk from a sheet of paper, the disk would have an area, and that is what we mean here.

Question 9

Given radius of a circle how do you calculate its area?

Answer 9

Given the radius of a circle, the area inside it can be calculated using the formula Area = πR 2 (that’s R square) where: R is the radius of the circle π is Pi, approximately

Question 10

What is a chord?

Answer 10

A line that links two points on a circle or curve. (pronounced “cord”)

Question 11

What is a tangent?

Answer 11

A line that contacts an arc or circle at only one point.

The line barely touches the circle at a single point. If the line were closer to the center of the circle, it would cut the circle in two places and would then be called a secant. In fact, you can think of the tangent as the limit case of a secant. As the secant line moves away from the center of the circle, the two points where it cuts the circle eventually merge into one and the line is then the tangent to the circle.

Question 12

What is secant?

Answer 12

A line that intersects a curve or circle at two points.

As you move one of the points P,Q, the secant will change accordingly. If the two points coincide at the same point, the secant becomes a tangent, since it now touches the circle at just one point.

Question 13

What is semicircle?

Answer 13

Half a circle. A closed shape consisting of half a circle and a diameter of that circle.

A semicircle is a half circle, formed by cutting a whole circle along a diameter line, as shown above. Any diameter of a circle cuts it into two equal semicircles.

Question 14

What is a sector?

Answer 14

The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

Question 15

What is Segment of a Circle?

Answer 15

The region between a chord of a circle and its associated arc.

Question 16

What is Inscribed Angle of a circle?

Answer 16

The angle subtended at a point on the circle by two given points on the circle.

See here for more.

Question 17

What is an Arc?

Answer 17

A portion of the circumference of a circle

Strictly speaking, an arc could be a portion of some other curved shape, such as an ellipse, but it almost always refers to a circle. To avoid all possible mistake, it is sometimes called a circular arc.

A straight line is drawn between the end points of the arc would be a chord of the circle.

If the arc length is exactly half the circle, this called a semicircular arc.

Question 18

What are major and minor Arcs?

Answer 18

Given two points on a circle, the minor arc is the shortest arc linking them. The major arc is the longest.

Two points lying on a circle actually define two arcs. The shortest is called the ‘minor arc’ the longer one is called the ‘major arc’. Typically, if you don’t specify which, readers will assume you mean the minor (shortest) arc. If there is a possibility of confusion, you should state which one you mean.

Question 19

What is Central Angle of a circle?

Answer 19

The angle subtended at the center of a circle by two given points on the circle.

The two points A and B can be isolated points, or they could be the end points of an arc or chord. When they are the end points of an arc, the angle is sometimes called the “arc central angle”

See here for more details.

Question 20

The central angle subtended by two points on a circle is twice the inscribed angle subtended by those points. True or False?

Answer 20

True

This is called Central Angle Theorem

See here for more details.

Question 21

The diameter of a circle always subtends a right angle to any point on the circle. True or False?

Answer 21

True

This is called Thale’s Theorem.

See here for more details.

Question 23

What is the angle inscribed in a semicircle?

Answer 23

Right angle.

This is special case of Thale’s theorem.

See here for more details.

Question 24

What is Angle Measure of an Arc?

Answer 24

The angle that an arc makes at the center of the circle of which it is a part.

Question 25

What is Arc length?

Answer 25

he distance along the curved line making up the arc

Question 26

What are adjacent arcs?

Answer 26

Non-overlapping arcs with the same radius and center, sharing a common endpoint.

Adjacent arcs are two arcs on the same circle which

1. Do not overlap, and
2. Share a common end point.

This means they are, in effect, joined end to end to create a larger arc.

Question 27

What is an intercepted Arc?

Answer 27

That part of a circle that lies between two lines that intersect it.

When two straight lines cross a circle, the part of the circle between the intersection points is called the intercepted arc. The lines intercept, or ‘cut off’, the arc.

Usually the two lines are the arms of an angle, but this is not always the case.

See here for more details.

Question 28

What is the radius of an arc or a segment?

Answer 28

The radius of an arc or segment is the radius of the circle of which it is a part

Question 29

What is Sagitta?

Answer 29

The sagitta is the height of an arc.
It is the perpendicular from the midpoint of the arc’s chord to the arc itself.

see here for more details.