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:
Answer & explanation
Correct answer: option 2
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