Question

$AB$ is the diameter of a semicircle $k,C$ is an arbitrary point on the semicircle (other than $A$ or $B$) and $S$ is the center of the circle inscribed into triangle $ABC$ the measure of : ?

• A. angle $ASB$ changes as $C$ moves on $k$
• B. angle $ASB$ is the same for all positions of $C$ but it cannot be determined without knowing the radius
• C. angle $ASB={135}^o$ for all $C$
• D. angle $ASB={150}^o$ for all $C$

Answer 1

The correct option is B angle $ASB$ is the same for all positions of $C$ but it cannot be determined without knowing the radius

Since $\measuredangle C$ is constant (i.e., $90°$) hence $\measuredangle ASB$ will also be constant but will be different for different values of radius of semi circle.

$\therefore$ Option B is correct.