Question

In the given figure, CD is a direct common tangent to two circles intersecting each other at A and B, then $\angle CAD+\angle CBD=$?

• A. ${120}^{\circ }$
• B. ${90}^{\circ }$
• C. ${360}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is D ${180}^{\circ }$

$\angle CAB=\angle BCDand\angle DAB=\angle BDC\therefore \angle CAD=\angle CAB+\angle DAB=\angle BCD+\angle BDC\Rightarrow \angle CAD=\angle BCD+\angle BDC\therefore \angle CAD+\angle CBD=\angle BCD+\angle BDC+\angle CBD={180}^{\circ }$