Question

In the given figure, AOB is a diameter of the circle with centre 0 and 2 AOC = 100°, find 2 BDC.
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Answer 1

Answer:

BDC = 40°

Step-by-step explanation:

ADB = 90° (Angle in semicircle)

ADC = 50°

BDC = 90- 50 = 40°

Hope it will be helpful

Answer 2

Answer :

∡ BDC = 40°

Step-by-step explanation

Construction :

Line from point A to point D (Line AD)

Proof :

∡ AOC = 2 × ∡ ADC (Reason - angles at the center of the circle is equal to twice the angle at the circumference)

100° = 2 × ∡ ADC

∡ ADC = 100° ÷ 2 = 50°

In Δ ADB :

∡ BDC + ∡ CDA = 90° (∡s in a semi-circle)

∡ BDC + 50° = 90°

∡ BDC = 90° - 50°

∡ BDC = 40°