Math 9 - Ms. Ko's Website



Exploring Angles in a Circle – 10.1 Notes

Naming angles: an angle is made up of 2 straight lines join the lines we label them with _____________________. This is used for naming our angle with the symbol ____ in front.

Example 1: Name the angles

Parts of a circle

|Chord |Arc |

| |[pic] |

| |An arc is a portion of the circumference. A major arc is an arc |

| |which covers more than half the circumference; a minor arc covers |

| |less than half the circumference. |

| | |

| | |

| | |

| | |

|A line segment connecting any two points on a circle is called a ________.| |

|In the figure above, AB is a chord. The longest chord (goes through the | |

|center of a circle) is the _______________ | |

|The radius is not a chord because it does not _______________________ | |

|Inscribed Angle |Central Angle |

|[pic] |[pic] |

|[pic] is an _________ angle. Its vertex is on the circle and its arms are|[pic] is a _____________angle. Its vertex is at the center and |

|__________. [pic] is said to subtend arc AB (or chord AB) |its arms are _________. [pic] is said to subtend arc EG (or chord|

| |EG) |

Practice: Name the angles that are:

a) Inscribed angles

b) Central angles

Properties of Inscribed and Central Angles

Inscribed angles subtending the same arc are _______________.

The measure of the central angle is _____________ the measure of the inscribed angle subtending the same arc. This could also be stated as the inscribed angle is _________ the central angle subtending the same arc.

Practice: Indicate in the diagrams below which angles have the relationship that one is twice the other.

|[pic] |[pic] |[pic] |[pic] |

Inscribed Angle on a Diameter

|[pic] |What type of angle is [pic]? |

| | |

| |How big is [pic]? |

| | |

| |What is the relationship between [pic] and [pic] ? |

| | |

| | |

| |An inscribed angle subtending a diameter is _________. |

Example 2: Determine the size of each of the angles (In each of the diagrams O is the center)

|[pic] |[pic] |[pic] |

| | | |

| | | |

|[pic] |[pic] |[pic] |

| | | |

Example 3: Point D is the centre of the circle. Diameter AB = 10, Chord AC = 6

a) What is the measure of angle ACB?

b) What is the length of the chord BC?

Example 4: Determine the length of line BC.

Assignment: textbook page 382-384 #3, 4, 6, 7, 10-13

Review Angles

Complementary Angles: angles that add up to ____. This is normally denoted with the symbol ______.

Supplementary Angles: angles that add up to ____.

Practice: Find the measure of each required angle.

Angles in a triangle: all the angles in a triangle, add to _____.

Practice: Find the measure of the missing angle in the triangles.

Angles at a point: all the angles at a point, add to ______.

Vertically Opposite: angles that are vertically opposite are __________.

Practice: Find the measure of the missing angles.

Assignment: worksheet

Quiz next day

Exploring Chord Properties – 10.2 Notes

Perpendicular bisector of a chord: a line that passes through the centre of a circle and is ______________________ to a chord bisects the chord.

Example 1: Radius CD bisects chord AB. Chord AB measures 8 cm. The radius of the circle is 5 cm. What is the length of CE?

Example 2: Radius CH bisects chord FG. Chord FG measures 12 cm. The radius of the circle measures 10 cm. What is the length of CJ?

Example 3: For the following diagrams, determine the value of x.

|a. |b. |

|[pic] |[pic] |

|c. |d. |

|[pic] |[pic] |

Example 4: The cross section of the pipe to the right shows some water still in the pipe. The horizontal distance across the water is 10 cm, and the inner diameter of the pipe is 14 cm. What is the maximum depth of the water in the pipe? Answer to the nearest tenth of a cm.

[pic]

Assignment: textbook page 389-391#4, 5, 7-12

10.3 – Tangents to a Circle – Notes

Definitions:

Tangent Line – a line that touches a circle at _______________

Point of Tangency – the point where the line touches the circle is called the point of tangency

Tangent to a Circle – if a radius or diameter meets a tangent line that at the point of tangency will form ______.

Example 1: Using the diagram to the right, determine:

| |[pic] |

|AD = __________ | |

|[pic]______ | |

|[pic]________ | |

|AB = _________ | |

|AE = _________ | |

Practice: Determine the length x:

[pic]

Example 2: Determine the length x:

[pic]

Example 3: Determine the angle [pic] for the following diagram:

[pic][pic]

Practice:

In the diagram shown, AB is a tangent to the circle at point D, BE contains the diameter FE, and ................
................

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