Question

In a circle with a radius of 10 cm. XY and PQ are two parallel chords 12 cm and 16 cm in length, respectively. The two chords are situated on the opposite sides of the centre. The distance between the chords is:
1. 14 cm
2. 18 cm
3. 12.80 cm
4. 12 cm

Answer 1

Correct Answer - Option 1 : 14 cm

Given:

Radius of circle = 10 cm

Length of XY = 12 CM

Length of PQ = 16 cm

Formula used:

AC² = AB² + BC² 

where, AB, BC - Sides of right - angled triangle, AC - Hypotenuse of right - angled triangle 

Calculation:

Let O be the center of circle

In ΔOAP,

OP² = OA² + AP²

⇒ (10)² = OA² + (6)²

⇒ 100 = OA² + 36

⇒ OA² = 64

⇒ OA = 8 cm

Similarly, in ΔOBR,

OR² = OB² + BR²

⇒ (10)² = OB² + (8)²

⇒ 100 = OB² + 64

⇒ OB² = 36

⇒ OB = 6 cm

Now, 

OA + OB = (8 + 6) CM

⇒ 14 cm

∴ The distance between the chords is 14 cm