Question

AB is the diameter of the circle O .CD is a chord which is equal to the radius in length. AC and BD are produced to meet at P .Then angle APB will be of?​

Answer 1

Step-by-step explanation:

Join OC,OD and BC

In ∆OCD, we have

OC = OD = CD (Each equal to radius) ∴∆ODC is an equilateral ∆.

∠COD = 600

Also, ∠COD = 2∠CBD

⇒ 600 = 2∠CBD ⇒ ∠CBD = 300

Since ∠ACB is angle in a semi-circle.

∠ACB = 900

⇒ ∠BCE = 1800 - ∠ACB = 1800 - 900 = 900

Thus, in △BCE,we have

∠BCE = 900 and ∠CBE = 300

∴ ∠BCE + ∠CEB + ∠CBE = 1800

⇒ 900 + ∠CEB + 300 = 180 ⇒

∠CEB = 60°

Hence, ∠AEB = ∠CEB = 60°