Solve this: â ‹Q13 In the above figure, AB and AC are equal chords and â ‹OD - Maths - Practical Geometry

Question

Solve this:

â€‹Q13 In the above figure, AB   and  
AC   are equal chords and â€‹ OD is
perpendicular to â€‹ AC If ∠ COD = 60°,
then the angle between the chords is _____________

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a437d7759683%20png">
Construction : Join AO and OBConsider, △AOB and △AOCWe have,AB=AC givenBO=CO radius of circleOA=OA common△AOB ≅ △AOC    SSS criteria∠BOA=∠COAConsider △AOD and △CODOD=OD common∠ODA=∠ODC=90°OA=OC   radius of circleSo, △AOD ≅ △COD    RHS criteria⇒∠AOD=∠COD 
1Now, ∠AOC=∠AOD+∠COD⇒∠AOC=2∠COD   using 1=2×60°=120°and ∠BOA=∠COA=120°Now ∠BOA+∠COA+∠BOC=360°    complete angle⇒∠BOC=360°-240°⇒∠BOC=120°Angles between the chords =∠BAO+∠CAO=∠BACNow, ∠BAC=12∠BOC=120°2=60° 
(angle
which
is subtended
by an arc
at the centre of
a circle is double
the size of the angle
subtended at any
point on the circumference)
Regards

Solve this: ​Q13. In the above figure, AB and AC are equal chords and ​ OD is perpendicular to ​ AC . If ∠ COD = 60°, then the angle between the chords is _____________.

Solve this:

Q13. In the above figure, $AB and AC$ are equal chords and $OD$ is perpendicular to $AC$ . If $∠$ COD = 60°, then the angle between the chords is _____________.