Question

Two parallel chords of length 8cm and 6cm of a circle are separated by a distance of 1cm. The radius of the circle is

Answer 1

Answer:

The radius of the circle is 5

Step

OC = R

OB = r

OP = a

OQ = a + 1

PC = 8/2 = 4

QB = 6/2 = 3

Using Pythagoras theorem

r =$\sqrt{3^{2} + (a+1)^{2} }$

R = $\sqrt{4^{2} + (a)^{2} }$                            . : r=R

$3^{2} + (a+1)^{2} = 4 ^{2} + a^{2}$

$a^{2} + 2a + 1 = 16 - 9 \\\\2a = 7 - 1\\a = 6/2 \\a = 3$

R = $= \sqrt{4^{2} + 3^{2} } \\= \sqrt{16 + 9} \\= \sqrt{25} \\= 5$