Q. 75.0( 1 Vote )

Construct a cyclic quadrilateral ABCD, given AB = 6 cm, ABC = 70°, BC = 5 cm and ACD = 30°

Answer :

We need to construct the required quadrilateral, when three sides and one diagonal of a cyclic quadrilateral are given.


Steps of construction:


Step 1: Draw a line segment AB = 6 cm.



Step 2: Through A draw BX such that ABX = 70°



Step 3: With B as centre and radius 5 cm, draw an arc intersecting BX at C and join BC.



Step 4: Draw the perpendicular bisectors of AB and BC intersecting each other at O.



Step 5: With O as centre and OA ( = OB =OC ) as radius, draw the circumcircle of Δ ABC.



Step 6: From C, draw CY such that ACD =30° , which intersects the circle at D.



Step 7: Join AD.



Thus, ABCD is the required cyclic quadrilateral.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Some Interesting Proofs in GeometrySome Interesting Proofs in GeometrySome Interesting Proofs in Geometry36 mins
Section FormulaSection FormulaSection Formula30 mins
Previous Year RMO QuestionsPrevious Year RMO QuestionsPrevious Year RMO Questions43 mins
NCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for BoardsNCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in TrianglesKnow About Important Proofs in TrianglesKnow About Important Proofs in Triangles33 mins
Champ Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsChamp Quiz | Previous Year NTSE QuestionsFREE Class
Measuring distance by Distance formulaMeasuring distance by Distance formulaMeasuring distance by Distance formula49 mins
Champ Quiz | Distance FormulaChamp Quiz | Distance FormulaChamp Quiz | Distance Formula30 mins
Set of Questions on Section FormulaSet of Questions on Section FormulaSet of Questions on Section Formula54 mins
Coordinate Geometry Important QuestionsCoordinate Geometry Important QuestionsCoordinate Geometry Important Questions38 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses