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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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O1 மற்றும் O2 ஆகியவற்றை மையங்களாகக் கொண்ட இரண்டு வட்டங்களின் நேரடி பொதுவான தொடுகோடு PQ ஆகும், அவை A என்ற புள்ளியில் வெளிப்படையாக ஒன்றையொன்று தொடுகின்றன. வட்டங்களின் ஆரங்கள் முறையே 11 செ.மீ மற்றும் 4 செ.மீ ஆகும். PQ இன் நீளத்தைக் காண்க.
211 செ.மீ
311 செ.மீ
411 செ.மீ
511 செ.மீ
411 செ.மீ
For circles touching externally, the direct common tangent length is twice the geometric mean of the radii, simply 2 times the square root of (11 multiplied by 4).
Two externally touching circles have radii r1 = 11 cm and r2 = 4 cm.
L=2r1×r2
For circles touching externally, the direct common tangent length is twice the geometric mean of the radii, simply 2 times the square root of (11 multiplied by 4).
Confusing the formula for direct common tangent (2r1r2) with the formula for transverse common tangent (2d2−(r1+r2)2).
Identify given parameters
The radii of the two circles are r1=11 cm and r2=4 cm. Since they touch externally, the distance between centers d=r1+r2=15 cm.
r1=11,r2=4
Apply Direct Common Tangent Formula
The length L of a direct common tangent for two circles touching externally is given by L=2r1×r2.
L=2r1×r2
Calculate the Result
Substitute the radii values into the formula: L=211×4=244. Simplifying the square root, 44=4×11=211. Thus, L=2×211=411 cm.
L=411
C is correct because the direct common tangent length calculated using 2r1r2 is 411 cm.
This concept is frequently tested alongside the distance between centers of intersecting circles or internal common tangents in competitive geometry.