Question

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​

Answer 1

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 2

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.