taiwan-gsat 2021 Q3

taiwan-gsat · Other · gsat__math 5 marks Sine and Cosine Rules Circumradius or incircle radius computation

As shown in the figure, $\triangle A B C$ is an acute triangle, $P$ is a point outside the circumcircle $\Gamma$ of $\triangle A B C$, and both $\overline { P B }$ and $\overline { P C }$ are tangent to circle $\Gamma$. Let $\angle B P C = \theta$. What is the value of $\cos A$?
(1) $\sin 2 \theta$
(2) $\frac { \sin \theta } { 2 }$
(3) $\sin \frac { \theta } { 2 }$
(4) $\frac { \cos \theta } { 2 }$
(5) $\cos \frac { \theta } { 2 }$

As shown in the figure, $\triangle A B C$ is an acute triangle, $P$ is a point outside the circumcircle $\Gamma$ of $\triangle A B C$, and both $\overline { P B }$ and $\overline { P C }$ are tangent to circle $\Gamma$. Let $\angle B P C = \theta$. What is the value of $\cos A$?\\
(1) $\sin 2 \theta$\\
(2) $\frac { \sin \theta } { 2 }$\\
(3) $\sin \frac { \theta } { 2 }$\\
(4) $\frac { \cos \theta } { 2 }$\\
(5) $\cos \frac { \theta } { 2 }$

Paper Questions

QA QB QC QD QE QF QG Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13