Circles C-1 amp- nbsp-C-2 externally touch each other and they both internally touch another circle nbsp-C-3- The radii of nbsp-C-1 amp- nbsp-C-2 are nbsp-4 and nbsp-10 respectiveley- and the centers of the three circles are collinear- A chord of nbsp-C-3 is a transverse common tangent to the circles nbsp-C-1 and nbsp-C-2- Find the length of the chord144-10-8-5-None of these

The correct option is D None of theseO_3P=r_3=10+10+4+42=14 O_3R=14 4 4=6 PR=√(14^2 6^2)=4√(10) PQ=8√(10) units. ...

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Standard XII

Mathematics

Length of Common Chord

Circles C_1 ...

Question

Circles $C_{1}$ & $C_{2}$ externally touch each other and they both internally touch another circle $C_{3}$ . The radii of $C_{1}$ & $C_{2}$ are $4$ and $10$ respectiveley, and the centers of the three circles are collinear. A chord of $C_{3}$ is a transverse common tangent to the circles $C_{1}$ and $C_{2}$ . Find the length of the chord

4 \sqrt{10}

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14

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8 \sqrt{5}

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None of these

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Solution

The correct option is D None of these
$O_{3} P = r_{3} = \frac{10 + 10 + 4 + 4}{2} = 14 O_{3} R = 14 - 4 - 4 = 6 P R = \sqrt{14^{2} - 6^{2}} = 4 \sqrt{10}$
$P Q = 8 \sqrt{10}$ units.

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Circles C1 & C2 externally touch each other and they both internally touch another circle C3. The radii of C1 & C2 are 4 and 10 respectiveley, and the centers of the three circles are collinear. A chord of C3 is a transverse common tangent to the circles C1 and C2. Find the length of the chord

The correct option is D None of theseO3P=r3=10+10+4+42=14O3R=14−4−4=6PR=√142−62=4√10 PQ=8√10 units.

The correct option is D None of these
$O_{3} P = r_{3} = \frac{10 + 10 + 4 + 4}{2} = 14 O_{3} R = 14 - 4 - 4 = 6 P R = \sqrt{14^{2} - 6^{2}} = 4 \sqrt{10}$
$P Q = 8 \sqrt{10}$ units.