LESSON 14-3:

A CAN’T, B CAN’T, SECANT!!!

SECANTS, TANGENTS AND ANGLES

• Up until now, we have discussed the tangents and inscribed angles of certain circles.

• Now, we can discuss secants and the angles created by them.

SECANTS, TANGENTS AND ANGLES

• Like a tangent line, we judge a secant line by the number of times it intersects the circle.

• THE NUMBER IS TWO!!!• When two secant lines intersect inside a circle

then the angle formed is related to the arcs they intercepts.

SECANTS, TANGENTS AND ANGLES• Theorem 14-8: If two secants or chords

intersect in the interior of a circle, then the measure of an angle formed is one half the sum of the measure of the arcs intercepted by the angle and it’s vertical angle.

SECANTS, TANGENTS AND ANGLES

• So let’s solve for the angles below.

A

C

B

DX

40⁰

110⁰

50⁰

160⁰

SECANTS, TANGENTS AND ANGLES

• What about this? Could you find ALL interior angles?

A

C

B

DX

35⁰65⁰

SECANTS, TANGENTS AND ANGLES• Not only to secants interact with each other.• Secants and tangents can intersect each other

too!• What is the relationship here?

SECANTS, TANGENTS AND ANGLES

• If a secant and tangent intersect at the point of tangency, then the measure of the angles will be half the measure of the arcs they intersect.

SECANTS, TANGENTS AND ANGLES

• Using the given information, find all missing angles and arcs in the figure below.

120⁰

SECANTS, TANGENTS AND ANGLES

• So we’ve dealt with angles on the interior of a circle and ones directly on the circle…

• ..but what about those on the exterior of a circle?

SECANTS, TANGENTS AND ANGLES

• These angles can be formed of the intersections of two secants, two tangents or one of each.

SECANTS, TANGENTS AND ANGLES

• Theorem 14-9: When any of these is the case, the angle measure can be found by taking half the difference of the two intercepted arcs.

SECANTS, TANGENTS AND ANGLES

• Find the measure of angle P below.

P30⁰

100⁰

𝑚<𝑃=12(100−30)

SECANTS, TANGENTS AND ANGLES

• Find the measure of angle P below.

P30⁰

100⁰

𝑚<𝑃=12(100−30)

M<P = 35

SECANTS, TANGENTS AND ANGLES• Find the measure of arc PO below…

P

30⁰40⁰

O40

SECANTS, TANGENTS AND ANGLES• Find the measure of arc PO below…

P

30⁰40⁰

O40

m = 130

SECANTS, TANGENTS AND ANGLES

• Today, you will need to use the information I have given you in many ways!