Tangents drawn from an external point P touches the circle with radius 5 cm with centre O at T. If OP intersects circle at B and PT = 12cm then find BT.
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BT = 20/√13 if Tangents drawn from an external point P touches the circle with radius 5 cm with centre O at T. If OP intersects circle at B and PT = 12cm
Step-by-step explanation:
OP² = PT² + OT²
OT = Radius = 5 cm
PT = 12 cm Given
=> OP² = 12² + 5²
=> OP² = 13²
=> OP = 13 cm
OP = OB + PB
OB = Radius = 5 cm
=> 13 = 5 + PB
=> PB = 8 cm
Cos∠POT = OT/OP
=> Cos∠POT = 5/13
=> Cos∠BOT = 5/13
in ΔBOT
OB = OT = 5 cm
Cos∠BOT = 5/13
BT² = OB² + OT² - 2 OB * OT Cos∠BOT
=> BT² = 5² + 5² - 2 * 5² (5/13)
=> BT² = 50 - 50 (5/13)
=> BT² = 50(1 - 5/13)
=> BT² = 50(8/13)
=> BT² = 400/13
=> BT = 20/√13
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BT = 20/√13 if Tangents drawn from an external point P touches the circle with radius 5 cm with centre O at T. If OP intersects circle at B and PT = 12cm
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