In ΔABC, AB = AC. A circle drawn through B touches AC at D and intersect AB at P. If D is the mid point of AC and AP 2.5 cm, then AB is equal to:

9 cm 10 cm 7.5 cm 12.5 cm

10 cm

AB = AC AC = 2AD As we know, \( {AD }^{2 } \) = AP x AB = \( {AD }^{2 } \) = 2.5 x AC = \( {AD }^{2 } \) = 2.5 x 2AD AD = 5 cm = AC = 2 x 5 = 10 cm Therefore, AB = AC = 10 cm