Embibe Experts Solutions for Exercise 1: ICSE-2019

Use ruler and compass only for answering the question.

Draw a circle of radius $4 \mathrm{cm}$. Mark the centre as $\mathrm{O}$. Mark a point $\mathrm{P}$ outside the circle at a distance of $7 \mathrm{cm}$ from the centre. Construct two tangents to the circle from the external point $\mathrm{P}$.

Measure and write down the length of any one tangent.

Using a ruler and a compass only construct a semi-circle with diameter $\mathrm{BC}=7 \mathrm{cm}$. Locate a point $A$ on the circumference of the semi-circle such that $A$ is equidistant from $B$ and $C$. Complete the cyclic quadrilateral $ABCD$, such that $D$ is equidistant from $AB$ and $BC$. Measure $\angle ADC$ and write it down.

Using ruler and compass construct a triangle $ABC$ where $AB=3 \mathrm{cm}, BC=4 \mathrm{cm}$ and$\angle ABC=90°$ . Hence construct a circle circumscribing the triangle $ABC$. Measure and write down the radius of the circle.

Use ruler and compass for the question. Construct a circle of radius $4.5 \mathrm{cm}$. Draw a chord $AB=6 \mathrm{cm}$.

Find the locus of points equidistant from $A$ and $B$. Mark the point where it meets the circle as $D$.

Use ruler and compass for this question. Construct a circle of radius $4.5 \mathrm{cm}$. Draw a chord. $\mathrm{AB}=6 \mathrm{cm}$. Find the locus of points equidistant from $\mathrm{A}$ and $\mathrm{B}$.
Mark the point where it meets the circle as $\mathrm{D}$. Join $\mathrm{AD}$ and find the locus of points which are equidistant from $\mathrm{AD} \text{and} \mathrm{AB}$. Mark the point where it meets the circle as $\mathrm{C}$.

A circle of radius $4.5 cm$ is drawn with chord $AB 6 cm$. $D$ is the locus of points of $A$ and $B$. $C$ is the locus of points of $AD$ and $AB$. Join $BC$ and $CD$. Measure and write down the length of side $CD$ of the quadrilateral $ABCD$.​

Using ruler and compass only, construct a $△ABC$ such that $BC=5 \mathrm{cm}, AB=6.5 \mathrm{cm}$ and $\angle ABC=120°$. Construct a circumcircle of$△ABC$.

Using ruler and compass only, construct a $∆ABC$ such that $BC=5 \mathrm{cm}$ and $AB=6.5 \mathrm{cm}$ and $\angle ABC=120°$. Construct a cyclic quadrilateral $ABCD$, such that $D$ is equidistant from $AB$ and $BC$.