HOW TO FIND RADIUS WHEN LENGTH OF TWO PARALLEL CHORDS ARE GIVEN

About "How to find radius when length of two parallel chords are given"

How to find radius when length of two parallel chords are given ?

Here we are going to see some examples problems on finding radius when length of two parallel chords are given.

Example 1 :

AB and CD are two parallel chords of a circle which are on either sides of the centre. Such that AB = 10 cm and CD = 24 cm. Find the radius if the distance between AB and CD is 17 cm.

Solution :

Consider the right triangles OEB and OFD,

In triangle OEB,

OB2  =  OE2 + EB2

OB2  =  x2 + 52  ---(1)

In triangle OFD,

OD2  =  OF2 + FD2

OD2 = (17-x)2 + 122 ---(2)

OB = OD (radius of the given circle)

(1)  =  (2)  

x2 + 52  =  (17-x)2 + 122

x2 + 52  =  172 + x2 - 2(17) x + 122

x2 + 25  =  289 + x2 - 34x + 144

x2 - x2 + 34x + 25 - 144 - 289  =  0

34x - 408  =  0

34(x - 12)  =  0

x  =  12 cm

By applying the value of x in the 1st equation, we get

OB2  =  122 + 52 

OB2  =  144 + 25  =  169

OB  =  √169  =  13 cm

Example 2 :

In the figure given below, AB and CD are two parallel chords of a circle with centre O and radius 5 cm such that AB = 6 cm and CD = 8 cm. If OP  AB and CD = OQ determine the length of PQ.

Solution :

Here we have two right triangles,

Triangle OPB and triangle OQD.

OB =  OD  =  radius of the circle  =  5 cm

In Δ OPB,

OB2  =  OP2 + PB2

OB2  =  OP2 + PB2

52  =  OP2 + 32

OP2  =  25 - 9

OP2  =  16

OP  =  √16

OP  =  4 cm

OD2  =  OQ2 + QD2

52  =  OQ2 + 42

25  =  OQ2 + 16

OQ2  =  25 - 16

OQ2  =  9

OQ  =  √9

OQ  =  3 cm

PQ  =  OP - OQ

  =  4 - 3

  =  1 cm

Hence the length of PQ is 1 cm

Example 3 :

In the figure given below, AB and CD are two parallel chords of a circle with centre O and radius 5 cm. Such that AB = 8 cm and CD = 6 cm. If OP = AB and OQ   CD.determine the length PQ.

Solution : 

Consider the triangles APO and COQ

OA  =  OC  =  radius of the circle  =  5 cm

AP  =  PB  =  4 cm

CQ  =  QD  =  3 cm

In triangle APO,

OA2  =  AP2 + PO2

52  =  42 + PO2

 PO  =  √(25 - 16)

 PO  =  √9

PO  =  3 cm

In triangle COQ,

OC2  =  OQ2 + CQ2

52  =  OQ2 + 32

OQ  =  √(25 - 9)

OQ  =  √16

OQ  =  4 cm

PQ  =  PO + OQ

  =  3 + 4

  =  7 cm

Hence the length of PQ is 7 cm.

After having gone through the stuff given above, we hope that the students would have understood "How to find radius when length of two parallel chords are given"

Apart from the stuff given above, if you want to know more about "How to find radius when length of two parallel chords are given".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...