Since, △ABC is an isosceles triangle, where AC=BC. Therefore, CD is the median and the perpendicular to AB. Since, length of centroid from the vertex =
2
3
of median ∴ Median (CD)=
8×3
2
=12cm and AD=
AB
2
=
10
2
=5cm Now, in right angle triangle ADC, AC2=AD2+CD2 [By Pythagoras theorem] ⇒AC2=(5)2+(12)2 =25+144=169 ∴AC=√169=13cm