Circle p is tangent to the x-axis and the y-axis. if the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.

 The length of the chord AB is √2 r units.

Step-by-step explanation: Given in the question that Circle P is tangent to the X-axis at the point A and tangent to the Y-axis at the point B.

Also, the co-ordinates of centre of the circle P are C(r, r). See the attached image below.

We are to find the length of the chord AB, with end-points A and B as the points of tangency.

From the figure, we note that

the co-ordinates of the points A and B are  (0, r) and (r, 0) respectively.

As the X-axis and Y-axis are perpendicular to each other, so the lines parallel to them, OB and OA are also perpendicular to each other.

That is, ∠ACB = 90°.

This implies that the triangle ACB is a right-angled triangle.

Now, using Pythagoras theorem in ΔACB, we have

The lengths of the line segments CA and CB are calculated, using distance formula, as follows:

From equation (i), we get

Thus, the length of the chord AB is √2 r units.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

555.99.

step-by-step explanation:

hope this