Question

) Point P and Q are the centres of externally at point M. Line ND is a tangent to the bigger circle and intersect smaller circle at point C. If QN=3, PQ=9, then find the length of NC, ND and CD. ​

Answer 1

Answer:

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Answer 2

Answer:

NC= $3\sqrt{3}$cm

ND= $6\sqrt{3}$cm

CD= $3\sqrt{3}$cm

Step-by-step explanation:

since, NA=3cm then QM=NA=3cm

so, PM=PD=radius of the bigger circle =6 cm

from ΔPDN, applying Pythagoras theorem

ND²=PN²-PD²= 144-36=108

ND=$6\sqrt{3}cm$

Now, as we know that angle made by the diameter of the circle at the circumference of the circle is 90° so that CM⊥NP

ΔNCM≈ ΔNDP

$\frac{NP}{NM} =\frac{ND}{NC}$

$\frac{12}{6} =\frac{6\sqrt{3} }{x}\\ x=3\sqrt{3}cm$

So, NC= $3\sqrt{3}cm$, CD=$3\sqrt{3}cm$, ND=$6\sqrt{3}cm$

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