CDS Model Paper 4 Mathematics

Let O be the centre of circle and AB be the chord of an are.
Given that
Length of chord AB=x, Radius of circle OA=z and height of an are‌M‌N=y AM=MB=

x

2

∵OM⊥AB
and OM=ON−MN=z−y [∵ON=z (radius) and MN=y]
In ΔOMA,OA2=OM2+AM2
[by Pythagoras theorem]
⇒ z2=(z−y)2+(

x

2

)2
⇒z2=z2+y2−2yz+

x2

4

⇒ 2yz−y2=

x2

4

⇒ 4(2yz−y2)=x2
⇒ 4y(2z−y)=x2