Question

In the given figure, find whether the points A, B, C, D are concyclic, when (i) x = 70 (ii) x= 80.

• A. (i)Yes (ii)No
• B. (i)No (ii)Yes
• C. (i)No (ii)No
• D. (i)Yes (ii)Yes

Answer 1

Answer: (A)

(i)Yes (ii)No

For the points A, B, C, D to con cyclic then $\angle ABC+\angle ADC={180}^o$
$\angle ABC={180}^o-\angle EBC$ (linear pair)
$={180}^o-{110}^o$
$={70}^o$
(i) x = 70 and $\angle EBC={110}^o$
x= ${180}^o-\angle ADC$
$\angle ADC={180}^o-x={180}^o-{70}^o={110}^o$
$\angle ABC+\angle ADC={70}^o+{110}^o={180}^o$
yes, it is concyclic.
(ii) x = 80 and $\angle EBC={110}^o$
x= ${180}^o-\angle ADC$
$\angle ADC={180}^o-x={180}^o-{80}^o={100}^o$
$\angle ABC+\angle ADC={80}^o+{110}^o={190}^o$
No, it is not concyclic.