### Circles R Us

Today we started class by Mr. K. putting up questions on the board. This was the first question:

To find line AO we used the Pythagorean Theorem (a² + b² = c²). If you plug in the numbers you get:

5² + 3² = c²

25 + 9 = c²

34 = c²

√34 = c

You know that line AB is 10 because line AC and line CB are congruent; and you know they are congruent because of the perpendicular bisector theorem.

This was the second question:

We know that line OE is a radius and we know that the radius is 23. So we subtract line CE from OE and get 10 (23 – 13 = 10). We know that line OC is perpendicular to line AB because of the perpendicular bisector theorem. In order to get line AB we must use the Pythagorean Theorem to get line CB. Once you know line CB you also know line AC because they are congruent. If you do everything properly you find that line CB is √429 or 20.71 if you round it off. Then you know that line AB is 2√429 or 41.42.

This was the third question:

To find line OC we used the Pythagorean Theorem and we got √203. Since line OC is perpendicular to line AB we know that line AC is congruent to line CB because of the perpendicular bisector theorem. The answer is 22 (11 + 11 = 22).

Mr. K. showed us a different way of solving these questions by using a chart with two columns, one that says statement and the other that says reason. This is how it would look like for the first question:

This is how it would look like for the second question:

This is how it would look like for the third question:

The fourth question was:

A chord that is 10 cm long is 12 cm away from the centre of a circle. Find the length of the radius.To solve this question we drew a picture and this is how our picture looked like:

We got that from the information given to us and by using the statement and reason chart.

The last question was:

The diameter of a circle is 20 cm. A chord is 8cm from the centre. How long is the chord?

For this question we also drew a picture, we went fairly quickly with this question so here is the picture:

If you are still confused, maybe this can help you. We drew what was already given to us which were a chord that was 8cm from the centre and a 20cm diameter. Then we drew a radius connecting to point C, which was 10cm. Then we used the Pythagorean Theorem to find line BC and got 6. Once you know that it’s 6, you also know that line AB is , then you add 6 and 6 together and get 12.

After all of that Mr. K. gave us two investigations to do and showed us how to construct perpendicular bisectors. The two investigations are for homework if you didn’t finish them in class and Exercise 31 is also for homework.***Reminders***

*You only have to use the chart when you are asked to justify your reasoning.

**Be careful about putting exact answers and/or approximations.

***You can use your statement as a reason after you have proved it.

**Use different colours with your circles.

*When drawing a radius imagine an infinite number of radii coming out from the centre and see which one connects with another point.

Lastly, the next scribe is:

## 3 Comments:

good job aichelle ! haha .. holy just had to make a banner for craigs name =( .. haha where's mmine =P

Ha Ha Ha? Great scribe post Aichelle. Copy's my name. lol. Hahaha. Circles R Us. Hahahaha. Great job in explaining it too. It's like I was in class again. Hah. Crazy. Nice banner Aichelle. Craig's the next scribe. Hahaha. I wanna be the scribe. Er... Maybe not. lol. Ok. I'm out.

If any textbook publishing company reads this you just might get a job offer. ;-)

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