If two arcs of a circle are congruent, then their corresponding chords are equal. Prove it.

Find the mean of the following numbers:

$$\begin{gathered} 16 14 12 8 23 26 18 20 \\ 9 11 22 27 18 20 23 \end{gathered}$$

State the value of the mean when each of these numbers is decreased by $6$.

In $△ABC, \angle B=90°, AB=40$ and $AC+BC=80$. Find $\sin A$.

In $△ABC, \angle B=90°$, find the value of $\sin A\cos C+\cos A\sin C$.

Prove that $\tan \left(55°+x\right)=\cot \left(35°-x\right)$.

If $\sin \theta =\cos \theta$, find the value of $3{\tan }^2\theta +{\sin }^2\theta -1$.

Draw the graph of $2x-3y+6=0$. Hence, find the co-ordinates of points where the graph drawn meets the co-ordinates axes. 

Show that quadrilateral $ABCD$ with $A(3, 10), B(0,-2), C(1. 1)$and $D(4,4)$ is parallelogram.