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Draw perpendicular AD
In isosceles triangle ABC ,BD =CD=10 cm
In right angled triangle ABD use Pythagoras theorem ,h²=p² +b², therefore AD(p)=√676-100=√576=24

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Draw a perpendicular from A on to BC. It will meet BC at the center D of BC. This can be show n from the symmetry.

Apply Pythagoras formula in triangle ADB or ADC, 26² = AD² + (BC/2)² = AD² + 10²