Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Q 3. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
 

Answers (1)

best_answer

Given: two equal chords of a circle intersect within the circle.

To prove: the line joining the point of intersection to the centre makes equal angles with the chords.
i.e. $\angle \mathrm{OEM}=\angle \mathrm{OEN}$

Proof : 

Construction: Join OE and draw $O M \perp A B$ and $O N \perp C D$.
In $\triangle \mathrm{OME}$ and $\triangle \mathrm{ONE}$,
$\mathrm{AE}=\mathrm{AE} \quad$ (Common)
$\mathrm{OM}=\mathrm{ON} \quad$ (Equal chords of a circle are equidistant from the centre)
$\angle \mathrm{OME}=\angle \mathrm{ONE} \quad$ (Both are right-angled)
Thus, $\triangle \mathrm{OME} \cong \triangle \mathrm{ONE}$ (By RHS rule)
$\angle \mathrm{OEM}=\angle \mathrm{OEN}(\mathrm{CPCT})$

Posted by

mansi

View full answer

Similar Questions

Trending Articles/News

anam-khan

Board Exam Date 2025 Live: Bihar Class 10, 12 model papers out, time table soon; updates on CBSE, UP

Latest Question