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THE RADII OF TWO CONCENTRIC CIRCLES ARE 13CM AND 8CM.AB IS A DIAMETER OF THE BIGGER CIRCLE.BD IS A TANGENT TO THE SMALLER CIRCLE TOUCHING IT AT D.FIND THE LENGTH AD. |
 construction: OM || BD STEPS : By BPT when OM||BD, AO/BO = AM/DM But, AO = BO => AM/DM = 1 or AM = DM Also, angle MOD = angle BDO = 90o (alternate angles) Now, BD2 = OB2 - OD2 = 169 - 64 =105 or, BD = ?105 cm Again, since OM || BD so, by similarity OM/BD = AO/AB => OM = BD X AO / AB = ?105 x 13 / 26 = ?105 / 2 or, OM = ?105 / 2 So in triangle ODM DM = ?OM2 + OD2 = ?105/4 + 64 = ?105 + 256 / 2 = ?361 / 2 or, DM = ?361 / 2 Hence, AD = 2 DM = ?361 = 9 |
