Two parallel chords are drawn in a circle of

diameter 300 cm. The length of one chord is

24.0 cm and the distance between the two

chords is 21.0 cm; find the length of the other

chord.

### Asked by siddeshmankar90.9spicertl | 6th Feb, 2021, 02:16: PM

Expert Answer:

###
Let AB = 24 cm be the first chord and CD be the second chord in the circle with centre O.
P and Q are on AB and CD bisecting them respectively.
So, AP = PB = 12 cm
In triangle APO, by Pythagoras theorem we have
PO^{2} = AO^{2} - AP^{2} = 15^{2} - 12^{2} = 81
Therefore, PO = 9 cm
So, we get OQ = 21 - 9 = 12 cm
In triangle COQ, by Pythagoras theorem we have
CQ^{2} = CO^{2} - OQ^{2} = 15^{2} - 12^{2} = 81
Therefore, CQ = 9 cm
Thus, CD = 2CQ = 18 cm

^{2}= AO

^{2}- AP

^{2}= 15

^{2}- 12

^{2}= 81

In triangle COQ, by Pythagoras theorem we have

CQ

^{2}= CO^{2}- OQ^{2}= 15^{2}- 12^{2}= 81Therefore, CQ = 9 cm

Thus, CD = 2CQ = 18 cm

### Answered by Renu Varma | 9th Feb, 2021, 12:55: PM

- In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm ar drawn. Find the distance between the chords if both the chords are (i) on the opposite sides of the centre (ii) on the same side of the centre .,:,entre.
- in a circle of radius 17cm ,two parallel chords of lenghts 30cm and 16 cm are drawn. Find the distance between the chords, iif both the chords are on the opposite sides of a circentre and onthe same side of the circle
- Class 9 project on circle cm graph
- In the given figure, angle DBC = 58 and BD ia a diameter of the circle. find (i) angle BDC (ii) angle BEC (iii) angle BAC
- In the figure, AB is parallel to DC, angle BCE = 80 and angle BAC = 25. Find (i) angle CAD (ii) angle CBD (iii) angle ADC
- In the given figure,O is the centre of the circle, angle AOB = 30 and angle OCB= 40 calculate angle AOC
- in the given figure ABCDE id a pentagon inscribed in a circle. If AB=BC=CD, angle BCD= 110 and angle BAE= 120 find (i) angle ABC (ii) angle CDE (iii) angle AED (iv) angle EAD
- In the given figure two chords AB and CD of a circle intersect at a point P. If AB = CD, prove that arc AD = arc CB
- In the given figure, two chords AC and BD of a circle intersect at E. if arc AB = arc CB, prove that BE = EC and AE = ED

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change