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ankur

· started a discussion

· 1 Months ago

wrong solution (Question: 113128.0 )

answer is d you did mistake in the last two steps of solution

Question:
Two concentric circles with centre C have radii r1 and r2 such that (r2 - r1) > 0. CA and CB are the common lined radii of the circles. If tangent at A is drawn to meet the bigger circle at the point D, then the length BD is given by:
Options:
A) \(\sqrt{2r_1(r_2-r_1)}\)
B) \(\sqrt{2r_2(r_2-r_1)}\)
C) \(\sqrt{2r_1(r_2+r_1)}\)
D) \(\sqrt{2r_2(r_2+r_1)}\)
Solution:
Ans: (b) 


It is given that

CA = r1, CD = r2

\(\therefore AD=\sqrt[]{CD^2-CA^2}\)

From \(\triangle\)ABD

BD2 = AB2 + AD2

= (r2-r1)2 + (r22 -r12)

= r22 + r12 + 2r2r1 + (r22-r12)

= 2r2 - (r2-r1)

\(\therefore AD=\sqrt{2r_2(r_2-r_1)}\) 

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Given answer is correct.
Keep learning,
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