O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 3: Chapter Test

Give all the names that apply to this given figure.

$\mathrm{D}$ is a point on the base $\mathrm{BC}$ of an isosceles triangle $\mathrm{ABC}$ in which $\mathrm{AB}=\mathrm{AC}$. The triangle $\mathrm{ADE}$ is drawn such that $\mathrm{AD}=\mathrm{AE}$, $\angle \mathrm{DAE}=\angle \mathrm{BAC}$ and $\mathrm{D},\mathrm{E}$ are opposite sides of $\mathrm{AC}$. Prove that $\mathrm{AC}$ bisects $\angle \mathrm{BCE}$.

In the given figure, which is not drawn accurately, $\angle \mathrm{BAD}=59°, \angle \mathrm{DAC}=32°$ and $\mathrm{AD}=\mathrm{BD}$. Calculate the value of the angle $\mathrm{ACB}$ and state, giving reasons, which is greater, $\mathrm{BD} \mathrm{or} \mathrm{DC}$.

In given figure, $\mathrm{ABCD}$ is an isosceles trapezium. Find the values of $x$ and $y$.

If the length of $AB$ is $k \mathrm{cm}$, find the value of $k$

The central angle of a minor arc is an acute angle.

Any two points on a circle determine a minor arc and a major arc.

In a circle, the perpendicular bisector of a chord must pass through the centre of the circle.