Maharashtra Board Solutions for Chapter: Circle, Exercise 1: Practice set 6.1

Distance of chord $\mathrm{AB}$ from the centre of a circle is $8$ $\text{cm}$. Length of the chord $\mathrm{AB}$ is $12$$\text{ cm}$. If the diameter of the circle is $k \mathrm{cm}$ then find $k$.

Diameter of a circle is $26$$\text{ cm}$ and length of a chord of the circle is $24$$\text{ cm}$. If the distance of the chord from the centre is $k \mathrm{cm}$ then find $k$.

Radius of a circle is $34 \text{cm}$ and the distance of the chord from the centre is $30$$\text{ cm}$, if the length of the chord is $k \mathrm{cm}$ then find $k$.

Radius of a circle with centre $O$ is $41$ units. Length of a chord $\mathrm{PQ}$ is $80$ units, if the distance of the chord from the centre of the circle is $k \mathrm{cm}$ then find $k$.

In figure given below, centre of two circles is $O$. Chord $\mathrm{AB}$ of bigger circle intersects the smaller circle in points $\mathrm{P}$ and $\mathrm{Q}$. Show that $\mathrm{AP}=\mathrm{BQ}$

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.