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AC = Length of the direct common tangents BD = Length of direct transverse tangents Let, the distance between two circles = x cm So, BD = √[x2 - (7 + 7)2] ⇒ 48 = √(x2 - 142) ⇒ 482 = x2 - 196 [Squaring on both sides] ⇒ 2304 = x2 - 196 ⇒ x2 = 2304 + 196 = 2500 ⇒ x = √2500 = 50 cm Also, AC = √[502 - (7 - 7)2] ⇒ AC = √(2500 - 0) = √2500 = 50 cm ∴ The length of BD is 48 cm, length of AC is 50 cm
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