Question

in figure the circles with centres A and B touch each other at E. line l is a common tangent which touches the circles at c and D respectively Find the length of CD if the radii of the circles are 4 cm and 6 cm

Answer 1

Construct AY || CD

=> BY = ( 6 - 4 ) = 2cm

Apply Pythagoras to get :

${x}^{2} + {2}^{2} = {10}^{2}$

$= > {x}^{2} = 96$

$= > x = \sqrt{96} = 4 \sqrt{6} cm$

Hence, CD = 4√6 cm

Answer 2

Answer: The answer is  4√6 cm.

Step-by-step explanation:  Given that CD is a tanggent to both the circles at C and D, so ∠ACD = ∠BDC = 90°.

As shown in the attached figure, AE is drawn parallel to CD so that the triangle ABP is a righ-angled triangle at angle APB. And, ACDP is a rectangle.

Also, BP = BD - PD = 6 - 4 = 2 cm.

From the given information, we have

AB = AE + EB = 4 + 6 = 10 cm.

Now, from the right-angled triangle ABP, using Pythagoras Theorem, we have

$AB^2=AP^2+PB^2\\\\\Rightarrow 10^2=AP^2+2^2\\\\\Rightarrow AP^2=100-4\\\\\Rightarrow AP^2=96\\\\\Rightarrow AP=4\sqrt6.$

Thus, CD = AP = 4√6 cm.