Question

in circle with Centre O, OM perpendicular to AB, OM is equal to 3 cm, AM is equal to 4 cm find QR
​

Answer 1

Answer:

Given o is the center of circle ,OM=3 cm and AB=8 cm

Join O to A and B

In figure OM show that the perpendicular from center O on cord AB

WE know that  Perpendicular from the Center of a Circle to a Chord Bisects the Chord.

Then AM=BM

So AM=BM=2AB=28=4cm

ΔAOM

(AO)2=(AM)2+(OM)2=(4)2+(3)2=16+9=25

⇒AO=5cm

Then AO is the radius of circle is 5 cm

Answer 2

Given

o is the center of circle ,OM=3 cm and AB=8 cm

Join O to A and B

In figure OM show that the perpendicular from center O on cord AB

WE know that Perpendicular from the Center of a Circle to a Chord Bisects the Chord.

Then AM=BM

So AM=BM= $\frac{ab}{2}$ = $\frac{8}{2}$

=4cm

ΔAOM(AO)²

=(AM)² +(OM)²

=(4) ²+(3) ²=16+9=25

⇒AO=5cm

Then AO is the radius of circle is 5 cm