Class 10 (PYQs 2023) Mathematics

Given:

1. Radius of larger (C)
R=5 cm

2. Radius of smaller (c)
r=3 cm

Let the chord of the larger circle be
𝐴
𝐵
, and it touches the smaller circle. That means the distance from the center to the chord is equal to the radius of the smaller circle, i.e., 3 cm.

Step-by-step Solution:

the perpendicular from the center to a chord bisects the chord.

So, we form a right triangle with:

1. One leg = distance from center to the chord = 3 cm

2. Hypotenuse = radius of the larger (C) = 5 cm

3. Half of the chord = unknown (let’s call it
𝑥
x)

Using the Pythagorean Theorem:

OP² = OS² + SP²

5² = 3² + SP²

SP² = 25 – 9

SP² = 16

SP = ±4

So, the full length of the chord is:

2x = 2 × 4 = 8 cm
​

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