In the given fig.,AB is the chord of the circle with centre O and BT is a tangent to the circle.If angle OAB = 35°,find the values of x and y.
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OA=OB [RADII]
ang OBA=ang OAB=30 deg [angles opp. to equal sides are equal]
ang OPB=90 deg [tangent]
ang OBA+ang ABP=90
30+ang ABP=90
ang ABP=90-30=60 deg
ang AOB= 180-(30+30)
120 [angle sum property of triangle]
saptarshi52:
nice process
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OAB=35
value of angle OBA=35° ( opposite angles to equal sides are equal)(equal sides are the radii OB &OA)
THEREFORE in triangle OAB
angle (OAB+OBA+BOA)=180°. (angle sum property of traingle)
therefore angle BOA =180-70=110
angle BOA is the central angle and angle Y is the inscribed angle therefore angle Y=110/2=55. (central angle is twice the inscribed angle)
BT Is the tangent to circle at B therefore OB(radius)is Perpendicular to the tangentBT
THEREFORE angle ( X +OBA)=90
therefore value of angle X=90-35=55
I hope this will help you
value of angle OBA=35° ( opposite angles to equal sides are equal)(equal sides are the radii OB &OA)
THEREFORE in triangle OAB
angle (OAB+OBA+BOA)=180°. (angle sum property of traingle)
therefore angle BOA =180-70=110
angle BOA is the central angle and angle Y is the inscribed angle therefore angle Y=110/2=55. (central angle is twice the inscribed angle)
BT Is the tangent to circle at B therefore OB(radius)is Perpendicular to the tangentBT
THEREFORE angle ( X +OBA)=90
therefore value of angle X=90-35=55
I hope this will help you
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