Question

In the following figure, centre of the circle is '$P$' joined with the points $Q$, $R$, $S$, $T$ on the same circle. If $\angle QPR={50}^o$, $\angle RPS={60}^o$ and $\angle SPT={100}^o$, find :
(a) $m\left(arcQRS\right)$
(b) $m\left(arcQST\right)$
(c) $m\left(arcRTS\right)$.

Answer 1

a) $m\left(arcQRS\right)=m\left(arcQR\right)+m\left(arcRS\right)$

$={50}^o+{60}^o$

$={110}^o$

(b) $m\left(arcQST\right)=m\left(arcQS\right)+m\left(arcST\right)$

$={110}^o+{100}^o$

$={210}^o$

(c) $m\left(arcRTS\right)+m\left(arcQRS\right)={360}^o$

$m\left(arcRTS\right)+{110}^o={360}^o$

$m\left(arcRTS\right)={360}^o-{110}^o$

$={250}^o$.