Okay so,
We already have ,
Both circles congruent,
that means their diameter and therefore radius are equal.
Which means,
AM= MB = CN = DN = 148/2 = 74 (radius of congruent Δs)
and
AL = BL = 140/2 = 70 (as a perpendicular on a chord from the center bisects the chord)
InΔ ΑLM and ΔCNQ seem to be congruent,
So,
ML = NQ ( by CPCT)
this means uf you found the value of ML somehow, you'll get the value of NQ.
So by applying pythagoras theorem in ΔALM
[tex] {AL}^{2} + {ML}^{2} = {AM}^{2} \\ \\ {ML}^{2} = {74}^{2} - {70}^{2} = (74 - 70)(74 + 70) \\ \\ {ML}^{2} = (4)(144) \\ ML = \sqrt{4 \times 144} = 24[/tex]
Hence, ML =24 cm =NQ
