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Quantitative Aptitude

Circles

In given figu...

Question

In given figure, O is the center of circle, chords AB and CD interact each other at P and PO bisect angle APD. If AB=8cm, OM. AB and OM. CD, find length of ND.

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Solution

Consider $Δ O M P$ and $Δ O N P$
OP = OP (common side)
<OPM = <OPN (given)
<ONP = <OMP
$∴ Δ O M P ≅ Δ O N P$
Therefore OM = ON
Since OM = ON AB = CD
CD = 8cm
$N D = \frac{8}{2} = 4 c m$

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In given figure, O is the center of circle, chords AB and CD interact each other at P and PO bisect angle APD. If AB=8cm, OM. AB and OM. CD, find length of ND.

Consider ΔOMP and ΔONP OP = OP (common side) <OPM = <OPN (given) <ONP = <OMP ∴ΔOMP≅ΔONP Therefore OM = ON Since OM = ON AB = CD CD = 8cm ND=82=4 cm

Consider $Δ O M P$ and $Δ O N P$
OP = OP (common side)
<OPM = <OPN (given)
<ONP = <OMP
$∴ Δ O M P ≅ Δ O N P$
Therefore OM = ON
Since OM = ON AB = CD
CD = 8cm
$N D = \frac{8}{2} = 4 c m$