Question

Q.1/10:The distance between the centres of two
equal circles each of radius 8 cm is 34 cm. The length
of a transverse tangent is:
8 से.मी. त्रिज्या वाले दो समान वृत्तों के केंद्रों के बीच की दूरी 34
सेमी है। एक अनुप्रस्थ स्पर्शरेखा की लंबाई है।
A.24cm
B.22 cm
C.28 cm
D.30 cm​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The distance between the centres of two equal circles each of radius 8 cm is 34 cm. The length of a transverse tangent is

A.24cm

B.22 cm

C.28 cm

D.30 cm

FORMULA TO BE IMPLEMENTED

If radius of two circles are R unit and r unit and distance between the centres is d unit then length

of a transverse tangent

$\sf{ = \sqrt{ {d}^{2} - {(R + r)}^{2} } }$

EVALUATION

Here it is given that the distance between the centres of two equal circles each of radius 8 cm is 34 cm.

Hence the length of a transverse tangent

$\sf{ = \sqrt{ {34}^{2} - {(8 + 8)}^{2} } } \: \: cm$

$\sf{ = \sqrt{ {34}^{2} - {16}^{2} } } \: \: cm$

$\sf{ = \sqrt{ (34 + 16) \times (34 - 16) } } \: \: cm$

$\sf{ = \sqrt{ 50 \times 18 } } \: \: cm$

$\sf{ = \sqrt{ 900 } } \: \: cm$

$\sf{ =30} \: \: cm$

FINAL ANSWER

Hence the correct option is D. 30 cm

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