Question

two circles of radius 4 cm and 5 cm touch each other externally EF is a direct common tanget to the circles. what is the length of EF ?​

Answer 1

Step-by-step explanation:

Let the two circles, C(Q,4) and C(R,1) touch externally. 

So the distance QR (distance between centers) = 5 

Let AB & CD be the two common tangents meet at P. 

So extending the line of centers, QR, it will also meet at P. 

Join AQ and BR; ∠QAP=∠RBP=900

[At point of contact, radius and tangent perpendicular to each other]. 

So of the above, we have two right triangles, QAP and RBP 

As ∠QAP=∠RBP=900 

∠APQ=∠BPR [Common] 

So the two triangles, APQ and BPR are similar [AA similarity] 

Hence, 

AQPQ=BRPR⇒AQQR+PR=BRPR⇒45+x=1x⇒x=35⇒PR=35

  

So taking ∠BPR=θ, 

sinθ=PRBR=351

Answer 2

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