Chapter 10 Formulas

Question 0

How do you find the measures of secant-secant, secant-tangent, and tangent-tangent angles?

Answer 0

Find the difference of the intercepted arcs and divide by two

Question 1

How do you find the measure of a chord-chord angle?

Answer 1

Add up the measure of the intercepted arcs then divide by two

Question 2

What do we know to be true if two inscribed or tangent-chord angles intercept the same arc?

Answer 2

That their angles are congruent

Question 3

What do we know to be true if an angle is inscribed in a semicircle?

Answer 3

It is a right angle

Question 4

What do we know to be true about the sum of the measures of a tangent-tangent angle and its minor arc?

Answer 4

Their sums are 180(th 92)

Question 5

Based on what we know from th 92, how do we find the measure of a tangent-tangent angle(x)?

Answer 5

Set up a system of equations with:
x= (360-y) -y
x= 180-y

Question 6

What do we know to be true about quadrilaterals inscribed in circles?

Answer 6

That their opposite angles are supplementary

Question 7

What do we know to be true about all parallelograms inscribed in circles?

Answer 7

That they must at least be a rectangle

Question 8

What does theorem 95 state?

Answer 8

That in a chord chord angle, the parts of one chord multiplied by each other are congruent to the parts of the other chord multiplied by each other

Question 9

What does theorem 96 state?

Answer 9

That in a secant-tangent angle, the outside part of the secant times the whole secant is congruent to the tangent squared

Question 10

What does theorem 97 state?

Answer 10

That in a secant-secant, the outside part of the first secant times the whole of the first secant is congruent to the outside part of the second secant times the whole of the second secant

Question 11

What is the arc length formula?

Answer 11

The length of the arc is congruent to the measure of the arc, divided by 360, times the circumference of the circle

Question 12

What does theorem 78 state?

Answer 12

If two chords of a circle are congruent then they are equidistant from the circles center

Question 13

What does theorem 79 state?

Answer 13

That if two central angles of the same or congruent circles, then their intercepted arcs are congruent.

Question 14

What do we know to be true if two arcs of a circle are congruent?

Answer 14

That their central angles are congruent

Question 15

What do we know to be true if two central angles of a circle are congruent?

Answer 15

That their corresponding chords are congruent

Question 16

What do we know to be true if two arcs of a circle are congruent?

Answer 16

That their corresponding chords are congruent

Question 17

What does the two tangent theorem state?

Answer 17

That if two tangent segments are drawn to a circle from an external point then they are congruent

Question 18

How do you find the measure of an inscribed angle?

Answer 18

Divide the measure of its intercepted arc by two