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$PQR$
Last updated date: 29th Mar 2023
•
Total views: 308.7k
•
Views today: 5.85k
Answer
308.7k+ views
Hint: Use the necessary tools to attempt construction problems. Follow the construction steps.
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.
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 \[\Delta PQR\].
\[m\angle AOC = {120^ \circ }\]
\[ \Rightarrow m\angle P = {180^ \circ } - {120^ \circ } = {60^ \circ }\] ……(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.
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
