Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle
Solution:
The chord of the larger circle is a tangent to the smaller circle as shown in the figure below.
PQ is a chord of a larger circle and a tangent of a smaller circle.
Tangent PQ is perpendicular to the radius at the point of contact S.
Therefore, ∠OSP = 90°
In ΔOSP (Right-angled triangle)
By the Pythagoras Theorem,
OP2 = OS2 + SP2
52 = 32 + SP2
SP2 = 25 - 9
SP2 = 16
SP = ± 4
SP is the length of the tangent and cannot be negative
Hence, SP = 4 cm.
QS = SP (Perpendicular from center bisects the chord considering QP to be the larger circle's chord)
Therefore, QS = SP = 4cm
Length of the chord PQ = QS + SP = 4 + 4
PQ = 8 cm
Therefore, the length of the chord of the larger circle is 8 cm.
☛ Check: NCERT Solutions Class 10 Maths Chapter 10
Video Solution:
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle
Maths NCERT Solutions Class 10 Chapter 10 Exercise 10.2 Question 7
Summary:
If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is 8 cm.
☛ Related Questions:
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