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In fig. there are two concentric circles with Centre O of radii 5cm and 3cm. From an
external point P, tangents PA and PB are drawn to these circles if AP = 12cm, find the
tangent length of BP.
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OA = 5 cm
OB = 3 cm
AP = 12 cm
BP = ?
We know that
At the point of contact, radius is perpendicular to tangent.
For circle 1, ΔOAP is right triangle
By Pythagoras theorem, ЁЭСВЁЭСГ2 = ЁЭСВЁЭР┤2 + ЁЭР┤ЁЭСГ2
⇒ ЁЭСВЁЭСГ2 = 52 + 122 = 25 + 144
= 169
⇒ OP = `sqrt(169)` = 13 ЁЭСРЁЭСЪ
For circle 2, ΔOBP is right triangle by Pythagoras theorem,
ЁЭСВЁЭСГ2 = ЁЭСВЁЭР╡2 + ЁЭР╡ЁЭСГ2
132 = 32 + ЁЭР╡ЁЭСГ2
ЁЭР╡ЁЭСГ2 = 169 − 9 = 160
ЁЭР╡ЁЭСГ = `sqrt(160) = 4sqrt(10)` ЁЭСРЁЭСЪ
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