Question

2. In a circle with centre P, the length of chord
AB is 40 cm. AB lies at a distance 21 cm
from the centre P, then find the diameter of
the circle.​

Answer 1

Required Answer:-

Question:

• In a circle with center P, the length of chord AB is 40 cm. AB lies at a distance 21 cm from the center P. Find the diameter of the circle.

Solution:

We know that,

"The straight line drawn from the centre of a circle to bisect a chord is perpendicular to the chord."

Therefore,

→ AB | OP (See the attachment)

→ AO = OB = AB/2 = 20 cm.

→ OP = 21 cm.

Applying Pythagoras theorem in ∆OPB, we get,

→ PB² = OP² + OB²

→ PB² = 21² + 20²

→ PB² = 441 + 400

→ PB² = 841

→ PB = √841

→ PB = 29 cm

Now, if we observe the figure, we can see that PB is the radius of the circle.

→ Diameter = 2PB

→ Diameter = 2 × 29 cm

→ Diameter = 58 cm.

★ Therefore, the diameter of the circle is 58 cm.

Answer:

• The diameter of the circle is 58 cm.