The points A(a, 0),B(0, b),C(c, 0),and D(0, d | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the origin be $O(0, 0)$. The points $A, B, C, D$ lie on the coordinate axes.According to the power of a point theorem,if two chords $AC$ and $

Vedclass · Accepted Answer

are concyclic

Vedclass · Answer

(D) Let the origin be $O(0, 0)$. The points $A, B, C, D$ lie on the coordinate axes.According to the power of a point theorem,if two chords $AC$ and $BD$ of a circle intersect at a point $O$,then $OA 	imes OC = OB 	imes OD$.Here,the coordinates are $A(a, 0)$,$C(c, 0)$,$B(0, b)$,and $D(0, d)$.The distances from the origin are $OA = |a|$,$OC = |c|$,$OB = |b|$,and $OD = |d|$.The condition given is $ac = bd$. If we consider the signed distances or the product of the coordinates,the condition $OA 	imes OC = OB 	imes OD$ is satisfied.Therefore,the points $A, B, C, D$ are concyclic.

The points $A(a, 0)$,$B(0, b)$,$C(c, 0)$,and $D(0, d)$ are such that $ac = bd$ and $a, b, c, d$ are all non-zero. Then the points:

Similar Questions

If two angles of $\triangle ABC$ are $45^{\circ}$ and $60^{\circ}$,then the ratio of the smallest side to the greatest side is:

Which of the following is an oxidizing agent?

Which among the following is $NOT$ a true statement for enantiomers?

Which of the following methods is used to obtain pure water from seawater?

$A$ rod of mass $M$ and length $l$ is suspended by two wires $P$ and $Q$. $A$ uniform magnetic field $B$ is directed into the page. When current $I$ flows through the rod,the tension in each supporting wire is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module