# Rectangle and circumscribed circle: 4th grade math test.

In this math test, the student will need to be focused and alert.
The circumscribed circle must be constructed with a ruler and compass. Using the properties of the course and the median from the right angle in a right triangle remains paramount. Read the entire statement to get a clear understanding.

## D.S : right triangle and circumscribed circle.

### Exercise 1 : 5 pts ”Demonstrate

Let C be a circle with center O and diameter 12 cm.

Let be the segments [AB]and [DC], two of its diameters.

1. Show that ADB is a right triangle (to be justified correctly).

2. What is the length of the median [OD] (to be justified correctly).

### Exercise 2: 5 pts.

Calculate the length AC, then EC.

Round the result to the hundredth
.

### Exercise 3 : 5 pts right-angled triangle

Draw a segment [AB] of 13 cm length.

Draw the circle(C1 ) of diameter [AB] and place a point M on the circle(C1 ) such that BM = 5 cm.

1) Make the figure and complete it afterwards.

2) Show that the triangle MAB is rectangular.

3) Calculate MA.

4) On the segment [AB], place the point I such that AI = 5.2 cm.

The circle(C2 ) of diameter [AI] cuts [AM] in J.

a) Show that the lines (IJ) and (MB) are parallel.

### Exercise 4: 5 pts.

John has to send a letter by mail.

Can he send this rectangular letter without folding it?

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