The side BA measures 11.53 units long.
Step-by-step explanation:
Step 1:
The side BP and PC are both the radii of the given circle. In the question, it is given that BP is 6 units long so PC is also equal to 6 units.
The line PA is split into two segments, PC and AC. It is given that AC is 7 units long.
So [tex]PA = PC+CA = 6+7 =13[/tex] units.
Step 2:
The triangle ABP is right-angled. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
[tex](PA)^{2} = (BP)^{2} + (BA)^{2} .[/tex]
Substituting the values we know, we get
[tex]13^{2} = 6^{2} + BA^{2} , BA^{2} = 13^{2} - 6^{2} ,[/tex]
[tex]BA^{2} = 169 - 36 = 133,[/tex]
[tex]BA = \sqrt{133} = 11.5325.[/tex]
Rounding off this value, we get BA measures 11.53 units long.
