Question

In a circle of radius 25 centimetres, the lengths of two parallel chord's are 30cm and 40 cm. If the chords are on the same side of the diameter, what is the distance between? If the chords are on either of the diameter, what is the distance between them?

Answer 1

Answer:

If the chords are on the same side of the diameter, then distance between them is 5cm. If the chords are on either of the diameter, then the distance between them is 35cm. Pls mark me as brainliest for the detailed answer.

Step-by-step explanation:

First we will find distance of each chord from center, then we will find each case. Pls draw the figure along with me to get it.

Smaller Chord:

A perpendicular line from center to a chord also bisects it (law)

So, draw a perpendicular line from center to the chord. Let it's lenght be x

x = distance between center and smaller chord

The point at which the perpendicular meets will be bisector, and each part length will be 15cm

Draw a radius (25cm) that joins at any 1 of the two endpoints of the smaller chord.

So, we can use pythagoras theorem to find x

x^2 = (25cm)^2 - (15cm)^2 = 400 cm^2

x = 20cm

Bigger Chord:

A perpendicular line from center to a chord also bisects it (law)

So, draw a perpendicular line from center to the chord. Let it's lenght be y

y = distance between center and bigger chord

The point at which the perpendicular meets will be bisector, and each part length will be 20cm

Draw a radius (25cm) that joins at any 1 of the two endpoints of the chord.

So, we can use pythagoras theorem to find y

y^2 = (25cm)^2 - (20cm)^2 = 225 cm^2

y = 15cm

Case 1:

If both parallel chords are on same side, distance between them = x - y = 5cm

Case 2:

If parallel chords are on different side, distance between them = x + y = 35cm