Question

AB and CD are two chords of a circle such that
AB = 18 cm, CD = 10 cm and AB is parallel
to CD. If the chords lie on the same side of the
centre and the distance between AB and CD is
2 cm, then which of the following is the
measure of length of the diameter of the circle?​

Answer 1

Answer:

diameter=30 cm

Step-by-step explanation:

construction:from centre o , draw a line perpendicular to AB and CD and then mark M on CD and N on AB

JOIN OB and OD.

MN=2 cm(given)

in triangle OND,

OM=X(LET)

OD=RADIUS

MD=5(AS, CD =10CM)

r^2=X^2+25. eqn. 1

Now,

in triangle ONB,

r^2=(X-2)^2+81

r^2=x^2-4x+4+81. eqn 2

here,

eqn 1 =eqn 2

x^2+25=x^2-4x+85

solve them to get X =15 CM = OM

IN TRIANGLE OMD,

OD^2=OM^2+MD^2

OD^2=15*15+5*5

OD=√250=5√10 cm

hence,

OD=RADIUS=5√10 CM

2*OD =DIAMETER=2*5√10=10√10CM