Himanshu
Last Activity: 8 Years ago
Please draw a figure while reading the following explanation.
Let the two chords be AB and CD of the circle with centre O, where AB>CD.
AOB + OAB + OBA = 180`
144` + OAB + OAB = 180`
OBA=OAB=18`
COD + OCD + ODC = 180`
72` + OCD + ODC = 180`
OCD = ODC = 54`
Let OX be the perpendicular to chords which cut AB at M and CD at N.
In triangle OAM, sin18` = OM / radius
radius × sin18`= OM ….i)
In triangle OBN, sin54` = ON / radius
radius × sin54` = ON ….ii)
Subtract i) and ii) ,
ON – OM = radius (sin18` – sin54`)
NM = radius / 2 (sin18` – sin54`= 2)
Hence, proved.
