Question

O is the Centre of the Ciele AB = 16cm,
cd= 14cm Seg OM Chord AB, Seg on
Chord If om
= 6cm then find on​

Answer 1

Answer:

Given- AB=16 cm and CD=14 cm are the chordsof a circle with centre at O.

OM(=6 cm)⊥AB at M and ON⊥CD at N.

To find out - 

If the length of ON=m cm, then m=? 

Solution-

We join OCand OA.

ΔOAM and ΔOCN are right ones, since OM⊥AB at M and ON⊥CD at N. 

Now AM=21AB=21×16 cm =8 cm and CN=21CD=21×14 cm =7 cm since the perpendicular from the centre of a circle to a chord bisects the latter.

So, in ΔOAM, by Pythagoras theorem, we have

OA=OM2+AM2=62+82 cm =10 cm and it\ is the radius of the circle.

∴OC=OA=10 cm. 

Again in ΔOCN, by Pythagoras theorem, we have

ON=OC2−CN2=102−72 cm 

Step-by-step explanation:

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