XY and AB are the two parallel chords of a circle 1 cm apart and are on the opposite sides of the centre If XY = 6 cm and AB = 8 cm, then find out the radius at the circle pls fast
Answers
Answer:
lution−
WedropperpendicularOMonABfromO.OMmeets
ABatM.
OMisextendedtomeetCDatN.
OA&OCarejoined.
∴OA&OCareradiiofthegivencircle.
OM⊥AB⟹∠AMO=90
o
=∠CNO
(correspondinganglesoftwoparallellines)
SoON⊥CD.
SoMNisthedistancebetweenAB&CD
i.eMN=1cm.
LetOM=xcm,thenON=(x+1)cm.
NowOM⊥AB⟹AM=
2
1
AB=
2
1
×8cm=4cm
(sincetheperpendicular,fromthecentreofacircle
toanyofitschords,bisectsthelatter).
AgainOM⊥AB.
∴ΔOAMisarightonewithOAashypotenuse.
So,byPythagorastheorem,weget
OA=
OM
2
+AM
2
=
x
2
+4
2
......(i).
Similarly,ON⊥CD⟹CN=
2
1
CD=
2
1
×6cm=3cm
(sincetheperpendicular,fromthecentreofacircle
toanyofitschords,bisectsthelatter).
AgainON⊥CD.
∴ΔOCNisarightonewithOC=OAashypotenuse.
So,byPythagorastheorem,weget
OC=OA=
ON
2
+CN
2
=
(x+1)
2
+3
2
......(ii).
Comparing(i)&(ii)weget
x
2
+4
2
=
(x+1)
2
+3
2
⟹2x=6
⟹x=3cm.
So,consideringΔOMA
∠OMA=90
o
.
∴ΔOMAisarightonewithOAashypotenuse.
So,byPythagorastheorem,weget
OA=
OM
2
+AM
2
=
x
2
+4
2
=
3
2
+4
2
cm=5cm.
Answer:
Chemistry, the science that deals with the properties, composition, and structure of substances (defined as elements and compounds), the transformations they undergo, and the energy that is released or absorbed during these processes.