Question

In the given figure, O is the centre of the circle, AB and CD are two chords such that OM > ON. Then which of the following is incorrect?

• A.
  $MC<AN$
• B.
  $MD<BN$
• C.
  $CD<AB$
• D.
  $MC<AN$

Answer 1

The correct option is D

$MC<AN$
$OM>ON\Rightarrow O{M}^2>O{N}^2\Rightarrow –O{M}^2<–O{N}^2\Rightarrow r^2–O{M}^2<r^2–O{N}^2(r=radius)\Rightarrow O{C}^2–O{M}^2<O{A}^2–O{N}^2(OC=OA=radius)\Rightarrow M{C}^2<A{N}^2\text{(By Pythagoras theorem)}\Rightarrow MC<AN$

Hence, the correct answer is option (d).