     Question Answers

# Draw a circle of radius $3cm$Draw triangle $ABC$ with this circle as circumcircle and angle ${50^ \circ },{60^ \circ }$ and ${70^ \circ }$.Construct triangle$PQR$, outside the circle, by drawing tangents to the circle at the points $A,B$and$C$.Find all angles of triangle$PQR$  Hint: Use the necessary tools to attempt construction problems. Follow the construction steps.

Steps of Construction:

Step #1: Draw a circle with centre $O$ having radius $3cm$.
Step #2: Take three points $A,B$and $C$ in the circle and join $A$ to the centre of the circle $O$.
Step #3: If $\angle BAC$ is to be${50^ \circ }$, should be${100^ \circ }$.
Step #4: If $\angle ABC$ is to be${60^ \circ }$, should be${120^ \circ }$.
Step #5: If $\angle ACB$ is to be${70^ \circ }$, should be${140^ \circ }$.
Step #6: Join the points B and C such that $m\angle AOC = {100^ \circ }$ and$m\angle BOC = {120^ \circ }$.
Thus, $\Delta ABC$is the required triangle.
Steps of Construction:

Step #1: Extend $OA$ and draw perpendicular to it through$A$.
Step #2: Extend $OB$ and draw perpendicular to it through$B$.
Step #3: In the same way draw a perpendicular from point $C$ through$OC$.
Let the points of intersection of these perpendicular be $P,Q$ and$R$, so we get the required $\Delta PQR$.
In the quadrilateral $PAOC$,

$m\angle AOC = {120^ \circ }$
$\Rightarrow m\angle P = {180^ \circ } - {120^ \circ } = {60^ \circ }$ ……(opposite angles of a quadrilateral are supplementary)
In the same way,
$\Rightarrow m\angle Q = {180^ \circ } - {140^ \circ } = {40^ \circ }$
And, $\Rightarrow m\angle R = {180^ \circ } - {100^ \circ } = {80^ \circ }$ Note: Use the necessary tools to attempt construction problems. Mistakes can be made in reading the angles wrongly on the instruments or incorrect dimensioning in the diagram.
View Notes
Construct Triangle Inscribed in a Circle  How to Draw a Perfect Circle    Construction of Triangle  Construction of Tangent to a Circle  Sides of a Triangle  Area of a Triangle  Properties of A Triangle  Altitude of a Triangle  Circumcenter of a Triangle  