Q. 75.0( 1 Vote )

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

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.  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 Geometry36 mins  Section Formula30 mins  Previous Year RMO Questions43 mins  NCERT | Most Important Proofs for Boards28 mins  Know About Important Proofs in Triangles33 mins  Champ Quiz | Previous Year NTSE QuestionsFREE Class  Measuring distance by Distance formula49 mins  Champ Quiz | Distance Formula30 mins  Set of Questions on Section Formula54 mins  Coordinate 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 view all courses 