Write True or False and justify your answer in each of the following:
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.
(B) The statement is False.
In $\triangle OAB$ and $\triangle OAC$,we have $OA = OA$ (common side) and $OB = OC$ (radii of the same circle).
However,the angles $\angle OAB$ and $\angle OAC$ are equal if and only if the chords $AB$ and $AC$ are equal in length $(AB = AC)$.
If the chords are of unequal lengths,the angles subtended by them at the center or the angles they make with the radius $OA$ will not be equal.
Therefore,the statement is not universally true.
In $\triangle OAB$ and $\triangle OAC$,we have $OA = OA$ (common side) and $OB = OC$ (radii of the same circle).
However,the angles $\angle OAB$ and $\angle OAC$ are equal if and only if the chords $AB$ and $AC$ are equal in length $(AB = AC)$.
If the chords are of unequal lengths,the angles subtended by them at the center or the angles they make with the radius $OA$ will not be equal.
Therefore,the statement is not universally true.
Explore More
Similar Questions
Write True or False and justify your answer in each of the following: Through three collinear points a circle can be drawn.
Easy
View SolutionThere is one and only one circle passing through all the vertices $A, B$ and $C$ of $\Delta ABC$. This circle is called the ............. of $\Delta ABC$.
Easy
View SolutionState whether the following statement is True or False and justify your answer: If $AOB$ is a diameter of a circle and $C$ is a point on the circle,then $AC^{2} + BC^{2} = AB^{2}$.
Medium
View SolutionIn the figure,$AB$ and $CD$ are two chords of a circle intersecting each other at point $E$. Prove that $\angle AEC = \frac{1}{2}$ (angle subtended by arc $CXA$ at the centre $+$ angle subtended by arc $DYB$ at the centre).
Difficult
View SolutionIn the figure,$O$ is the centre of the circle,$BD = OD$ and $CD \perp AB$. Find $\angle CAB$.
Difficult
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo