Chhattisgarh Board Solutions for Exercise 14: Exercise – 2

Two chords $\mathrm{AB}$ and $\mathrm{AC}$ of a circle are equal. Prove that centre of circle lies on the bisector of $\angle \mathrm{BAC}$.

Two parallel chords which are $10 \mathrm{cm}$ and $24 \mathrm{cm}$ long respectively lie on opposite sides of centre of a circle. The distance between chords is $17 \mathrm{cm}$. Find the diameter of circle.

Centre of a circle is $O$ and $PO$ is the angle bisector of $\angle APD$ (See in the figure). Prove $AB=CD$.

$\mathrm{O}$ and $\mathrm{C}$ are centres of two circles whose radii are $13 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively (see figure). If perpendicular bisector of $\mathrm{OC}$ meets on points $A$ and $B$ of the bigger circle then find the length of $\mathrm{AB}$.

Two equal chords $AB$ and $CD$ in a circle with centre at $O$ meet at right angle on point $E$. If $P$ and $Q$ are midpoints of chords $\mathrm{AB}$ and $\mathrm{CD}$ then prove that $OPEQ$ is a square.