Outcome E4: apply properties of circles

Nicole B

1. All chords that are the same distance from the center of a circle have the same length. Another way of writing this is, “All chords *equidistant* from the center of a circle are *congruent*.”

2. (Converse # 1) All chords that are the same length are the same distance from the center of the circle.

3. A line that is perpendicular to a chord of a circle and passes through the center of the circle bisects the chord.

4. (Converse #3) A line that is perpendicular to a chord of a circle and bisects the chord passes through the center of the circle.

5. The measure of an arc is equal to the measure of the central angle subtended by the arc.

(A **central angle** is an angle with its vertex in the center of a circle.)

6. The measure of an inscribed angle is half the measure of the central angle subtended by the same arc.

(An **inscribed angle** is an angle with its vertex on the circumference of a circle.)

7. All inscribed angles subtended by the same arc are equal.

8. The measure of An angle inscribed in a semi-circle is always 90°.

**1)A chord is 10cm from the centre of a circle that has a diameter of 50cm. How long is the chord?**

*5^2 + b^2=25^2*

* 25 + b^2=625*

* b^2=600*

* b=24.5 x 2 = 49*

*The chord is 49cm long.*

**2)In standard form a circle has an equation of (x-3)^2+(y-4)^2=36, what is the mid point of the circle?**

*The mid point of the circle is (3,4).*

*
*

## Comments (1)

## Anonymous said

at 7:06 pm on Jun 14, 2007

Nice Job Nicole. Very nice titles and use of colour. I think there's a mistake in your sample problem however.

You don't have permission to comment on this page.