Question

In the adjoining figure ,O is the centre of circle of radius of 5cm OP perpendicular to AB, OQ PERPENDICULAR to CD and AB parallel to CD if AB=8 and CD=6cm ,findPQ

Answer 1

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Answer 2

Step-by-step explanation:

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=21AB=21×6 cm =3 cm and CQ=21CD=21×8 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.