The correct option is
C 1 cm
Given-
AB=6 cm and
CD=8 cm are the chords of a circle of radius
5 cm with centre at
O.
OP⊥AB at M and OQ⊥CD at N.
To find out - the length of PQ=?
Solution-
We join OC and OA.
So, OC=OA=5 cm, since OC and OA are radii.
ΔOAP and ΔOCQ are right ones, since OP⊥AB at P and OQ⊥CD at Q.
Now AP=12AB=12×6 cm =3 cm and CQ=12CD=12×8 cm =4 cm, since the perpendicular from the centre of a circle to a chord bisects the latter.
So, in ΔOAP, by Pythagoras theorem, we have
OP=√OA2−AP2=√52−42 cm =3 cm
Again in ΔOCQ, by Pythagoras theorem, we have
OQ=√OC2−CQ2=√52−32 cm =4 cm.
∴PQ=OP−OQ=(4−3) cm =1 cm