Question

in a circle with Centre P chord of a circle ab equals to 8cm andradius equals to 8 cm then angle APB equals to​

Answer 1

Answer:

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=

2

1

AB=

2

1

×6 cm =3 cm and CQ=

2

1

CD=

2

1

×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=

OA

2

−AP

2

=

5

2

−4

2

cm =3 cm

Again in ΔOCQ, by Pythagoras theorem, we have

OQ=

OC

2

−CQ

2

=

5

2

−3

2

cm =4 cm.

∴PQ=OP−OQ=(4−3) cm =1 cm