Question

Two parallel chords PQ and MN are 3cm apart on the same side of a circle where PQ=7cm and MN=14cm. Calculate the radius of the circle.

Answer 1

The radius of the circle is approximately 7.16 cm.

Step-by-step explanation:

Let's denote the radius of the circle as r.

Since the parallel chords PQ and MN are 3 cm apart, we can draw a perpendicular line from the center of the circle to chord PQ. Let's call the point where this line intersects with chord PQ as point A. Now, we have a right triangle APQ with the hypotenuse PQ measuring 7 cm and the side AP (which is half of the distance between the chords) measuring 1.5 cm.

Using the Pythagorean theorem, we can find the radius of the circle:

r = √(AP2 + PQ2)

r = √(1.52 + 72)

r = √(2.25 + 49)

r = √51.25

r ≈ 7.16 cm (rounded to two decimal places)