А B C O D,AB=5см,PCOD=17,OD=?

We are given that AB = 5 cm and PCOD = 17.

To find OD, we need to use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In triangle PCOD, we can see that OD is the hypotenuse. So, let's label the other two sides as PO and PC.

Using the Pythagorean theorem, we have:

PC^2 + PO^2 = OD^2

We are given PCOD = 17, so we can write:

PC^2 + OD^2 = 17^2

We are also given that AB = 5 cm, and since AB is a straight line segment, it is equal to PC.

So, PC = AB = 5 cm.

Substituting PC = 5 cm, we have:

5^2 + OD^2 = 17^2

25 + OD^2 = 289

OD^2 = 289 - 25

OD^2 = 264

Taking the square root of both sides, we have:

OD = √264

Simplifying, we find:

OD ≈ 16.24 cm.

Therefore, OD is approximately equal to 16.24 cm.