Circle Properties

Question 1

Triangle in a circle where the diameter is one of the segments of the triangle

Answer 1

If a triangle is inside a circle and two of endpoints are on the diameter of the circle, then the angle on the circle itself is equal to 90 degrees

Question 2

Intersecting chord angles

Answer 2

The average of the arcs created by two intersecting chords equals the angle at the intersection between the chords

Question 3

When a chord intersects a tangent…

Answer 3

It creates an inscribed angle whose value is equal to half of the arc that it intercepts (just like every other inscribed angle)

Question 4

A central angle in a circle

Answer 4

has the same measurement as the arc it intercepts

Question 5

Chord segments

Answer 5

When two chords intersect each other, multiplying two segments of the same cord equals multiplying two segments of the other cord. (i.e. if one cord is split into a length of 5 and 4, and the other is split into 10 and x, then x must equal 2 because 54 = !0x)

Question 6

When a diameter perpendicularly intersects a chord…

Answer 6

…it splits that chord into two equal segments

Question 7

An inscribed angle…

Answer 7

…has half the measure of the arc it intercepts (in other words, the measure of the arc is twice as big as the inscribed angle)

Question 8

All radii are equal, which is important because…

Answer 8

…if you connect the end of the radii, it creates an isosceles triangle

Question 9

If two chords are equidistant from the center of a circle…

Answer 9

… those chords are congruent