Question

In the circle, O is the centre, chords AE = AD = DC and angle ABC= 56°. Find angle CBD, angle CBE, angle BOC and angle COD.
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Answer 1

Answer:

As angle in a semi - circle is 90∘,

∠AOB=∠ACB=90∘

In △ABC,∠ACB+∠ABC+∠CAB=180∘

⇒CAB=180−90−56=34∘

As ABCD is a cyclic quadrilateral

and sum of opposite angles =180∘

in a cyclic quadrilateral,

⇒∠ADC+∠ABC=180∘⇒∠ADC=124∘

⇒∠BDC=34∘

In △ADC,△ADC+∠DAC+∠DCA=180∘

(AD=DC)⇒124∘+2∠DAC=180∘

⇒∠DCA=28∘

In △BDC,∠BCD+∠CDB+∠CBD=180∘

(90+28)+34+∠CBD=180∘

∠CBD=180−152=28∘

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