In figure, 'O' is the centre of circle
Seg OP I chord AB,
AB = 16 cm, then find AP ?
O-a
A
B
Answers
Answer:
03 Visits remaining as a guest
You have limited access to toppr answr. Sign to unlock 35 lakh questions
What's your doubt?
Untagged
Bookmark
In fig, O is the centre of a circle AB=16 cm, CD=14 cm, seg OM ⊥ seg AB, seg ON ⊥ seg CD. If OM=6 cm, then length of seg ON is
m
cm. So, m is
184251
Expand-image
share
Share
Answer
Open in answr app
Open_in_app
Correct option is
B
m=51cm
2
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=
2
1
AB=
2
1
×16 cm =8 cm and CN=
2
1
CD=
2
1
×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=
OM
2
+AM
2
=
6
2
+8
2
cm =10 cm and it\ is the radius of the circle.
∴OC=OA=10 cm.
Again in ΔOCN, by Pythagoras theorem, we have
ON=
OC
2
−CN
2
=
10
2
−7
2
cm =
51
cm
But given that ON=
m
.
∴ m=51cm
2
Answer:
ans 16 because a.p ab = 16