PQ is a diameter of a circle and PS is a chord. If PQ is 82 cm and PS is 80 cm, the distance (in cm) of PS from the center of the circle is:

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Graduate Level) Official Paper (Held On: 20 Jun, 2024 Shift 3)

Answer 1

Given:

Diameter of the circle, PQ = 82 cm

Chord of the circle, PS = 80 cm

Formula Used:

Using the right triangle property in a circle:

If a chord is perpendicular to the diameter, the formula to find the distance from the center to the chord is:

Distance = \(\sqrt{r^2 - (c/2)^2}\)

Where, r = radius of the circle, c = length of the chord

Calculation:

F5 SSC Savita 12-8-24 D1

Radius, r = PQ / 2 = 82 / 2 = 41 cm

Half of the chord, c/2 = 80 / 2 = 40 cm

Distance from the center = \(\sqrt{41^2 - 40^2}\)

Distance = \(\sqrt{1681 - 1600}\)

Distance = \(\sqrt{81}\)

Distance = 9 cm

The distance of PS from the center of the circle is 9 cm.