Question

in the adjoining figure ab is a chord of length 16 cm of a circle with Centre O and radius 10cm the tangent at A and B intersect at the point P find the length of p a

Answer 1

Draw a line from point O which intersects AB at Q and OQ is perpendicular to AB.
AQ = BQ ( Bcz a perp. from centre of the circle to a chord, divide the chord equally)
In triangle AOQ
AO^2 = AQ^2 + OQ^2
10^2 = 8^2 + OQ^2
100 = 64 + OQ^2
OQ^2 = 100 - 64
OQ = under root 36
OQ = 6 cm
in triangle OQA and triangle OAP
OQ/ OA = AQ/PA
6/10 = 4/PA
PA = 40/6
PA = 20/3

Answer 2

Please see the attachment