Question

In the given figure AB is a chord of a circle with Centre O such that AB equal to 16 cm and radius of a circle is 10 cm. Tangents at A and B intersect each other at P. Find the length of PA.

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

Ab is a chord of length 16cm of a circle of radius

Step-by-step explanation:

OA =10 cm

Perpendicular from centre to the chord bisects the chord.

So

AM = MB = 8cm

Using Pythagoras Theorem in triangle AOM

So,

OM=6

Now,

Tan angle aob=4/3(LB/OL)

NOW AGAIN TANAOB=PB/OB=4/3

BY SOLVING ANSWER IS 4/3