Q. 104.3( 6 Votes )

Prove that a circle

Answer :

                                                    
In the figure ΔABC is an isosceles such that AB = BC. Circle C(O, r) is drawn on the side AB as diameter and intersecting side AC in D.
To Prove: AD = CD
Construction: Join B to D
Proof: ∠ADB = 90° (angle in a semi-circle)
Now in ΔABD and ΔBDC
AB = BC (given)
BD = BD (common)
∠ADB = ∠BDC (each 90°)
∴ ΔABD ≅ ΔBDC
∴ AD = CD

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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