the length of a tangent from a point A at distance 10cm from the centre of the circle is 6cm find the radius of the circle
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Let O be the centre of circle and Let P be a point such that,
OP = 10 cm.
Let PT be the tangent such that,
PT = 6 cm.
Join OT.
Now , PT is a tangent at T and OT is the radius thorough T.
Therefore,
OT perpendicular PT.
In the right ∆OTP , we have :
OP² = OT² + PT² [ By Pythagoras theroem ]
OT = √OP² - PT²
OT = ✓(10² - (6)²
OT = √100 - 36
OT = ✓64
OT = 8 cm.
Hence,
The radius of the circle is 8 cm.
OP = 10 cm.
Let PT be the tangent such that,
PT = 6 cm.
Join OT.
Now , PT is a tangent at T and OT is the radius thorough T.
Therefore,
OT perpendicular PT.
In the right ∆OTP , we have :
OP² = OT² + PT² [ By Pythagoras theroem ]
OT = √OP² - PT²
OT = ✓(10² - (6)²
OT = √100 - 36
OT = ✓64
OT = 8 cm.
Hence,
The radius of the circle is 8 cm.
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length of radius is equal to 8 .
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