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​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 _____________.

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Construction : Join AO and OBConsider, AOB and AOCWe have,AB=AC givenBO=CO radius of circleOA=OA commonAOB  AOC    SSS criteriaBOA=COAConsider AOD and CODOD=OD commonODA=ODC=90°OA=OC   radius of circleSo, AOD  COD    RHS criteriaAOD=COD ...1Now, AOC=AOD+CODAOC=2COD   using 1=2×60°=120°and BOA=COA=120°Now BOA+COA+BOC=360°    complete angleBOC=360°-240°BOC=120°Angles between the chords =BAO+CAO=BACNow, BAC=12BOC=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)

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