B Nirmala Shastry Solutions for Exercise 2: EXERCISE 14B

In the circle with centre $O$, $\angle BOD=160°$, chord $BC=$chord $CD$. Find $\angle BOC, \angle OBD, \angle OBC$ and $\angle CBD$.

$AB$ is a side of a regular hexagon and $BC$ is a side of a regular nonagon. Find $\angle BOC, \angle AOB, \angle OBC, \angle OAC$ and $\angle ABC$.

In the given figure, $A, B, C$ are three points on the circumference of a circle with centre $O$. $\mathrm{arc} \mathrm{AB}=2 \mathrm{arc} \mathrm{BC}$ and $\angle AOB=108°$. Calculate: (i) $\angle BOC,$(ii) $\angle OAB,$ (iii) $\angle OAC$, (iv) $\angle BAC$

In the circle,$O$ is the centre, chords $AE=AD=DC$ and $\angle ABC=56°$. Find: $\angle CBD,$$\angle CBE,$$\angle BOC$,$\angle COD$

In the semicircle with centre $O$, chords $PQ=QR=RS$. Find $\angle QOR, \angle OPR, \angle OPQ$ and $\angle QPR$.

In the circle with centre $O$, $AB=BC$ and $\angle AOC=140°$. Find $\angle BOC, \angle OAC, \angle OAB$ and $\angle BAC$.

$O$ is the centre of the circle. If $PS=QR$ and $\angle PQS=24°$. Find $\angle QPR, \angle OSQ, \angle POS$

In the circle with centre $O$, $BO\perp$diameter $AD$. Chord $BC=$chord $DE$. Find the angles $p, q, r$ and $\angle AOE$.