Question

অনুশীলনী 10.5
চিত্র 10.36 ত, A, B আৰু C তিনিটা বিন্দু O
কেন্দ্রবিশিষ্ট বৃত্তত অৱস্থিত যাতে ABOC = 30°
আৰু ZAOB = 60°। যদি বৃত্তটোৰ ABC চাপত
নথকা D এটা বিন্দু তেন্তে ZADC নির্ণয় কৰা।​

Answer 1

English Translation:

In fig 10.36, A, B and C are three points on a circle with centre O such that <BOC=30° and <AOB=60°. If D is a point on the circle other that are ABC, find the ∠ADC.

the ∠ADC = 45°

Given:

∠AOB = 60°

∠BOC= 30°

To find:

∠ADC =?

Solution:

Here,∠AOC = ∠AOB + ∠BOC

∠AOC = 90°  ( angle subtended at the centre of the circle)

∠AOC = 60°+30°

Since Arc ABC makes an angle of 90° at the centre of the circle.

∠ADC= 1/2∠AOC

Since the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining of the circle

∠ADC= 1/2(90°)

∠ADC= 45°

Hence, ∠ADC= 45°

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