0

Guest

Courses New

The circle which passes through the vertices a and c of a parallelogram OABC has a centre at O if BA produced meets the circle at D then prove that ABC=2 times of angle OCD

The circle which passes through the vertices a and c of a parallelogram OABC has a centre at O if BA produced meets the circle at D then prove that ABC=2 times of angle OCD

Grade:10

1 Answers

Arun
25758 Points
2 years ago
Question is to prove that ∠APD = ∠ADP
See the attached picture to represent the problem.  
ABCD is a parallelogram.  
=>Opposite angles are same.  
=>∠ABC = ∠ADC
=>∠BAD = ∠BCD
A circle is drawn in such a way that it passes through A, B and C.  
P is a point on circle intersecting with line CD.
ABCP is cyclic quadrilateral.  
(Circle is passing through all four vertices. A, B, C and P).
From the property of Cyclic Quadrilateral, ∠ABC + ∠APC = 180°.
(Opposite angles are supplementary)
∠APC + ∠APD = 180°. (Angle on straight line)
From above 2, we can derive  ∠ABC = ∠APD.  
∠ABC = ∠ADP = ∠APD.  
∠ADP = ∠APD.
 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on 10 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More