Question

In the given figure $\angle CAB={80}^{\circ },\angle CBA={55}^{\circ }and\angle DCA={45}^{\circ }$.The statement BD is the diameter is :

• A. False
• B. cannot be determined
• C. True
• D. Not Possible

Answer 1

The correct option is C True

$\angle BAC=\angle BDC={80}^{\circ }$ (Angle in the sum segment are equal )
In $△BAC,\angle ACB={180}^{\circ }-(\angle BAC+\angle CBA)$
$={180}^{\circ }-({80}^{\circ }+{55}^{\circ })$
$={180}^{\circ }-{135}^{\circ }={45}^{\circ }$
$\therefore \angle BCD=\angle BCA+\angle ACD={45}^{\circ }+{45}^{\circ }={90}^{\circ }$
$\Rightarrow BD$ is the diameter.(Angle in a semi-circle $={90}^{\circ }$)