Question

AB & CD are two chords such that AB= 10 cm,CD= 24 cm and AB parallel to CD the distance between chords is 17 cm. find the radius of the circle​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let r be the radius of the circle. Let OP and OQ

be perpendiculars drawn from O on CD and AB

respectively .

CP = 1/2 CD = 12cm

and AQ = 1/2AB = 5cm

In right triangle OPC,

OC*2 = OP*2 + CP*2 ( Pythagorean theorem)

or r*2 = d*2 + 144 .....(1)

In right triangle OQA,

OA*2 = OQ*2 + AQ*2

r*2 = (d+17)*2 + 25 ...(2)

From equation (1) &(2)

d*2 +144 = (d+17)*2 +25

d*2 + 144 = (d*2 + 289 + 34d) + 25 【Identity (a+b)*2 = a*2 + b*2 + 2ab】

d*2 +144 = d*2 + 289 + 34d +25

144 = 314 +34d

34d = 314 - !44

d = 170/34

d = 5 cm

r*2 = (5)*2 + (12)*2. 【From (1)】

r*2 = 25 + 144

r = √169

r = 13 cm

radius = 13cm

Hope u understand!!