Question

AB is a diameter. CD=4√5 ,PA=2cm. find diameter​

Answer 1

here AB the diameter cuts the chord CD into two equal halves

therefore PC=PD

$cd = 4 \sqrt{5} \\ pc = pd = \frac{4 \sqrt{5} }{2} \\ = 2 \sqrt{5}$

we have the relation

PA*PB=PC^2

$2 \times pb = {(2 \sqrt{5)} }^{2} \\ = 2 \times 2 \times \sqrt{5} \times \sqrt{5} \\ = 4 \times 5 \\ = 20 \\ pb = 20 \div 2 \\ = 10$

diameter AB=PA+PB

=2+10

=12cm