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Standard X

Mathematics

Lengths of Tangents Drawn from External Point

In Fig. 8.62,...

Question

In Fig. 8.62, there are two concetric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP=12 cm, find the length of BP.

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Solution

Sol:

In ΔOAP is a right angle at A then OP² = OA² + AP²

OA = 5 cm, OB = 3 cm and AP = 12 cm

OP² = 5² + 12² = 25 + 144 = 169

OP = 13 cm

In ΔOBP is a right angle at A then OP² = OB² + BP²

169 = 9 + BP²

BP²= 160

BP = 4√10 cm.

∴ length of BP = 4√10 cm.

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In Fig. 8.62, there are two concetric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP=12 cm, find the length of BP.

Sol: In ΔOAP is a right angle at A then OP2 = OA2 + AP2 OA = 5 cm, OB = 3 cm and AP = 12 cm OP2 = 52 + 122 = 25 + 144 = 169 OP = 13 cm In ΔOBP is a right angle at A then OP2 = OB2 + BP2 169 = 9 + BP2 BP2 = 160 BP = 4√10 cm. ∴ length of BP = 4√10 cm.

Sol:

In ΔOAP is a right angle at A then OP² = OA² + AP²

OA = 5 cm, OB = 3 cm and AP = 12 cm

OP² = 5² + 12² = 25 + 144 = 169

OP = 13 cm

In ΔOBP is a right angle at A then OP² = OB² + BP²

169 = 9 + BP²

BP²= 160

BP = 4√10 cm.

∴ length of BP = 4√10 cm.