Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle
Solution:
Given, two concentric circles with centre O
Radius of the outer circle = 5 cm
Chord AC is tangent to the inner circle.
The length of the chord, AC = 8 cm
We have to find the radius of the inner circle.
From the figure,
Let c₁ be the inner circle
Let c₂ be the outer circle with radius 5 cm.
Joining O to the chord AC which meets at D.
We know that the perpendicular drawn from the centre of a circle to the chord always bisects the chord.
So, OD ⟂ AC
Also, AD = DC = AC/2
AC/2 = 8/2 = 4 cm
So, AD = DC = 4 cm
Considering triangle OAD,
ODA is a right triangle with D at right angle.
AO² = AD² + OD²
OD = radius of inner circle
OA = radius of outer circle = 5 cm
AD = 4 cm
So, (5)² = (4)² + OD²
25 = 16 + OD²
OD² = 25 - 16
OD² = 9
Taking square root,
OD = 3 cm
Therefore, the radius of the inner circle is 3 cm.
✦ Try This: Out of the two concentric circles, the radius of the outer circle is 4 cm and the chord AC of length 9 cm is a tangent to the inner circle. Find the radius of the inner circle.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.3 Problem 1
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle
Summary:
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. The radius of the inner circle is 3 cm
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