Two parallel chords of a circle are respectively 46cm and 40cm long. If the radius of the circle is 25cm and the centre of the circle lies between the two chords, what is the distance between the chords?

SpotlessKing10

4 months ago

Alright, let’s take this step by step — this is a classic circle + chord question. No rush

Given:

Radius
𝑟
=
25
 
cm
r=25cm

Length of first chord
=
46
 
cm
=46cm

Length of second chord
=
40
 
cm
=40cm

Centre lies between the two chords (important!)

Key idea

For a chord of length
𝐿
L in a circle of radius
𝑟
r, the perpendicular distance
𝑑
d from the centre to the chord is given by:

𝑑
=
𝑟
2
−
(
𝐿
2
)
2
d=
r
2
−(
2
L
​

)
2
​

Distance of the 46 cm chord from the centre
46
2
=
23
2
46
​

=23
𝑑
1
=
25
2
−
23
2
d
1
​

=
25
2
−23
2
​

=
625
−
529
=
625−529
​

=
96
=
96
​

Distance of the 40 cm chord from the centre
40
2
=
20
2
40
​

=20
𝑑
2
=
25
2
−
20
2
d
2
​

=
25
2
−20
2
​

=
625
−
400
=
625−400
​

=
225
=
15
=
225
​

=15
Distance between the two chords

Since the centre is between them, we add the distances:

Distance between chords
=
96
+
15
Distance between chords=
96
​

+15
96
≈
9.8
96
​

≈9.8
=
9.8
+
15
=
24.8
 
cm
=9.8+15=24.8cm
Final Answer:
24.8
cm (approximately)
24.8 cm (approximately)

EM.O.J.I_u

1 year ago

no explanation

excel400

1 year ago

Form two right angled triangles by drawing a perpendicular line 'd' and connecting the radius to the end of both chords. Since the perpendicular line passes through the center of the circle, it can be said that it bisects the chord into equal parts.
For the triangle with adjacent 20cm (40cm/2):
.................. 25^2 = 20^2 + x^2 (using pythagoras theorem and assuming that the distance between the center of the circle and the 40cm chord is x)
................... 625 = 400 + x^2
................... x^2 = 625 - 400
................... x = sqrt(225)
................... x = 15

Let's call the distance between the center of the circle and the 46cm chord y
For the triangle with adjacent 23cm (46cm/2):
.................. 25^2 = 23^2 + y^2
.................. 625 = 529 + y^2
.................. y^2 = 625 - 529
.................. y = sqrt(96)
................. y = 4 sqrt(6)

d = x+y
d = 15 + 4 sqrt(6) cm

So, my brothers and sisters, our answer can only be found in the solution...

KlausMichealson

2 months ago

In the past question on the website the answer picked there was 15 meanwhile the answer is meant to be 22.

KumahJonathan

1 month ago

The answer isn't there and the nearest answer is 26 which is option D and now am marked wrong

AndroidSmart

1 year ago

The correct answer is B. 15cm.

Here's how to solve it:

Let's call the distance between the two chords "d". Since the centre of the circle lies between the two chords, we can draw a perpendicular line from the centre of the circle to each chord. This creates two right triangles with the radii as the hypotenuse and the distances from the centre to the chords as the legs.

Using the Pythagorean theorem, we can write:

r^2 = (c/2)^2 + (d/2)^2

where r is the radius, c is the length of the chord, and d is the distance between the chords.

Since we have two chords, we can write two equations:

25^2 = (46/2)^2 + (d/2)^2
25^2 = (40/2)^2 + (d/2)^2

Simplifying and solving for d, we get:

d = 15cm

Therefore, the distance between the two chords is 15cm.