Circles

Observation

Question

Move the slider and observe how the angles in the same segment of a circle are related.

Diameter

The angles subtended by the same chord in the same segment are equal.

Position of P

Position of chord

Find the value of x in the figure. O is the centre of the circle.

Oops!

You’ve missed something! Let’s go back to the observation tab and give it another shot!

60°

40°

45°

50°

Solution

• ∠BAN and ∠NMB are the angles subtended by the same segment BNMA.
• ∴ ∠BAN = ∠NMB = 30° [by theorem].
• Also, AB is the diameter. Hence,
  ∠ANB = 90°.
• In △ABN, ∠ANB = 90° and ∠BAN = 30°.
• ∴ ∠ANB + ∠BAN + x = 180°
   ⇒        90° + 30° + x = 180°
   ⇒                           x = 60°