In fig Op is equal to diameter of the circle. Prove that abp is a equilateral triangle..
sry abt the figure but i dnt know how to upload the figure
But its a circle with two tangents AP and BP... and joining OP, OA and OB ( o is the centre of the circle... )
let r be the radius of the circle
in right triangleOAP
sin tita=AO/OP =r/2r =1/2
therefore angle APO=30'
angleAPO =angleBPO =30'
angleAPB =30'+30' =60'
PA =PB (TANGENTS THEOREM)
ANGLE PAB= ANGLE PBA
angle PAB+ angle PBA + angle APB =180' (ANGLE SUM PROPERTY)
angle PAB+ angle PBA +60' =180'
angle PAB+ angle PBA =120'
angle PAB= angle PBA =60'
there fore triangle APB equilateral triangle as all anglas are 60'.