Question

1. In the given circle, O is the centre. Chords AD =CD, If ZABC = 40°, find ZABD, ZBOC and ZCOD. ​

Answer 1

Step-by-step explanation:

REF. Image.

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

∘