Question

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points without finding the centre of the circle.

Answer 1

by diameter property we can get the 4th point

Answer 2

Answer:

Step-by-step explanation:

Let A,B,C,D be the given point with B as centre and radius equal to AC draw an arc . With C as centre and AB as radius draw another arc, intersecting the previous arc at D. Then the required point is D

Proof:-

In ∆ABC and ∆DCB

AB=DC. (By construction)

AC=DB. (By construction)

BC=CB. ( Common)

Hence, ∆ABC congruence∆DCB

So, <BAC=<BDC. (Cpct)

These are angles in a same segment

So, ABCD is a cyclic quadrilateral

Proved