Q. 115.0( 2 Votes )

 Two circles are drawn on the sides AB and AC of DABC as diameters the circles intersect each other at a point D.

Answer :

In ΔABC,
AB is the diameter of the circle C(O, r) and AC is the diameter of the circle C'(O', r'). The circles intersect at D.
To Prove:   
∴D lies on BC.
Construction: Join A to D.
Proof: Angle in a semi-circle is 90°.
∴ ∠ADB = 90° and ∠ADC = 90°
Hence, ∠ADB + ∠ADC=180°
⇒ ∠BDC = 180°
Therefore, B, D, C are collinear i.e. D lies on BC.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
RD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma |  Extra Qs. of Cyclic QuadrilateralsRD Sharma | Extra Qs. of Cyclic Quadrilaterals31 mins
Important Questions on CirclesImportant Questions on CirclesImportant Questions on Circles29 mins
NCERT | Imp. Qs. on CirclesNCERT | Imp. Qs. on CirclesNCERT | Imp. Qs. on Circles43 mins
Quiz | Lets Roll on a CircleQuiz | Lets Roll on a CircleQuiz | Lets Roll on a Circle45 mins
Proof of Important Theorems of CirclesProof of Important Theorems of CirclesProof of Important Theorems of Circles45 mins
Concept of Cyclic QuadrilateralConcept of Cyclic QuadrilateralConcept of Cyclic Quadrilateral61 mins
Master Theorems in CirclesMaster Theorems in CirclesMaster Theorems in Circles42 mins
Genius Quiz | Rolling Around CirclesGenius Quiz | Rolling Around CirclesGenius Quiz | Rolling Around Circles49 mins
Proof of Important Theorems of CirclesProof of Important Theorems of CirclesProof of Important Theorems of Circles46 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