In the given diagram 'O' is the centre of the circle and AB is parallel to CD
AB = 24 cm and distance between the chords AB and CD is 17 cm. If the radius
of the circle is 13 cm, find the length of the chord CD.
Answers
Since op perpendicular to ab and oq perpendicular to cd nd ab parallel to cd
poq is a st. line
ab=10cm,cd=24cm nd pq is 17cm
ap=bp=half ab = 5cm and cq=dq=half cd =12cm
if oq=x cm ,then op= (17-x)cm
join oa nd oc
oa=oc=r(radius)
now in right angled triangle oap,
oa square=op square+ap square
=r square=(17-x)square+ 5square_ist equation
in right angled triangle ocq,
oc square=oq square+cq square
=r square=x square+12square_2nd equation
frm ist nd 2nd equations ,we get :
on solving we get x=5
r square=x square+12 square
r square=5 square+12 square
r square= 25+144
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Answer:
Since op perpendicular to ab and oq perpendicular to cd nd ab parallel to cd
poq is a st. line
ab=10cm,cd=24cm nd pq is 17cm
ap=bp=half ab = 5cm and cq=dq=half cd =12cm
if oq=x cm ,then op= (17-x)cm
join oa nd oc
oa=oc=r(radius)
now in right angled triangle oap,
oa square=op square+ap square
=r square=(17-x)square+ 5square_ist equation
in right angled triangle ocq,
oc square=oq square+cq square
=r square=x square+12square_2nd equation
frm ist nd 2nd equations ,we get :
on solving we get x=5
r square=x square+12 square
r square=5 square+12 square
r square= 25+144
r = 13cmr=13cm
radiusofthecircleis13cm.
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