Math CentralQuandaries & Queries


Question from arun, a student:

a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find are of the semi circle?

Hi Arun,

I drew a diagram of the situation you described.


Since the line segment ab is a diagonal of a circle and c is on the circumference, the angle bca is a right angle. You know the lengths of bc and ca so you can use Pythagoras theorem to find the length of the diagonal ab.


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