Question

A, B, C and D are points on a circle, centre O such that AC is a diameter of the circle. If $\angle BAD={75}^o$ and $\angle ACD={25}^o$. The magnitude of $\angle BDC$ is

• A. ${10}^o$
• B. ${15}^o$
• C. ${20}^o$
• D. ${25}^o$

Answer 1

The correct option is A ${10}^o$

$\angle ABD$ and $\angle ACD$ are made by the same arc AD

$⟹\angle ABD=25$

In $△ABD$

$\angle ABD+\angle ADB+\angle BAD=180$

$\angle ADB=180–75–25=80$

$\angle ADC=90$

$\angle ADB+\angle BDC=90$

$\angle BDC=90–80=10$