# <span lang="EN-US

(i)

Let radius OB = OD = 5 cm

Chord AB = 8 cm

Chord CD = 6 cm

BP = (1/2) AB

BP = (1/2) 8 = 4 cm

DQ = (1/2) CD

DQ = (1/2) 6 = 3 cm

In triangle OPB,

OP2 = OB2 - BP2

OP2 = 52 - 42

OP2= 25 - 16

OP2= 9

OP = 3 cm

In triangle OQD,

OQ2 = OD2 - DQ2

OQ2 = 52 - 32

OQ2= 25 - 9

OQ2= 16

OQ = 4 cm

Now,

PQ = OQ – OP = 4 – 3 = 1

Hence, distance between chords = 1 cm.

(ii)

Let radius OA = OC = 5 cm

Chord AB = 8 cm

Chord CD = 6 cm

AP = (1/2) AB

AP = (1/2) 8 = 4 cm

CQ = (1/2) CD

CQ = (1/2) 6 = 3 cm

In triangle OAP,

OP2 = OA2 - AP2

OP2 = 52 - 42

OP2= 25 - 16

OP2= 9

OP = 3 cm

In triangle OQD,

OQ2 = OC2 - CQ2

OQ2 = 52 - 32

OQ2= 25 - 9

OQ2= 16

OQ = 4 cm

Now,

PQ = OP + OQ = 3 + 4 = 7

Hence, distance between chords = 7 cm.

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