Question

AOB is a diameter of the circle and C,D,E are any three points on the semicircle. find the value of angle ACD + angle BED

Answer 1

Join AE.,

since, ACDE is a cyclic quadrilateral

angle ACD + angle AED = 180. _____(1)

Also, angle AEB = 90 ( angle in a semi circle) ______(2)

on adding equation 1 and 2 we get

angle ACD + angle AED + angle AEB = 180+90

angle ACD + angle BED = 270

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Answer 2

Answer:

270°

Step-by-step solution:

Given:

A circle centered at O has a diameter AB

To Find:

∠ACD + ∠DBE

Solution:

In the given figure ∠ACB = 90°   (Angle subtended by diameter)

Quadrilateral BCDE is cyclic as all vertices lie on the circle,

∴  ∠BCD + ∠DBE = 180° (Sum of opposite angles of a cyclic quadrilateral)

∠ACD = ∠ACB + ∠BCD

⇒ ∠ACD + ∠DBE = ∠ACB + ∠BCD + ∠DBE

⇒ ∠ACD + ∠DBE = 90° + 180°

⇒ ∠ACD + ∠DBE = 270°