The perpendicular from the centre of a circle to a chord, bisects the chord
so
PR=10
Then using pythagoras' theorum
$$\\12^2=10^2+x^2\\\\
144=100+x^2\\\\
44=x^2\\\\
x=\sqrt{44}\\\\
x=\sqrt4 \times \sqrt{11}\\\\
x= 2\sqrt{11} \;\;units\\
x= 2\sqrt{11} \;\;units\\
x=6.6332496\;units\\
x=6.63 \;\mbox{units to 2 decimal places}$$
Thanks Alan.
The perpendicular from the centre of a circle to a chord, bisects the chord
so
PR=10
Then using pythagoras' theorum
$$\\12^2=10^2+x^2\\\\
144=100+x^2\\\\
44=x^2\\\\
x=\sqrt{44}\\\\
x=\sqrt4 \times \sqrt{11}\\\\
x= 2\sqrt{11} \;\;units\\
x= 2\sqrt{11} \;\;units\\
x=6.6332496\;units\\
x=6.63 \;\mbox{units to 2 decimal places}$$
Thanks Alan.
Look carefully at the information you have in the diagram. With O as the centre of the circle and a right-angle at R, then length PR is half of length PQ, so PR is 10. This means you have a right-angled triangle with hypotenuse of length 12, one side of length 10 and one of length x. From Pythagoras we know that:
x2 + 102 = 122. Can you take it from there?
Ok, no need to - Melody's already done it!! Apart from expressing the answer as a decimal rounded to two places.
You know Rose those first two joint lines on the top of the circle seemed to me as if they were someones mustaches when i saw them first!