Thread: circle

In the figure , AB and CD are chords of a circle with centre O . They intersect at right angle at E . THe perpendiculars from teh centre O meet AB at H and CD at K . Given that EA=27 cm , EB=13 cm , and ED=9cm , prove that CD=30 cm . Hence calculate OH and the radius of the circle .

Hello thereddevils

Originally Posted by thereddevils

In the figure , AB and CD are chords of a circle with centre O . They intersect at right angle at E . THe perpendiculars from teh centre O meet AB at H and CD at K . Given that EA=27 cm , EB=13 cm , and ED=9cm , prove that CD=30 cm . Hence calculate OH and the radius of the circle .

There's a theorem - see for instance here - that tells you that in the diagram you have here:

(It derives from the fact that the triangles and are similar. Can you see why? Hint: use angles in the same segment.)

So, if we plug in the numbers given:

cm

Now (although it doesn't look like it in your diagram) is the mid-point of (and the mid-point of ). So cm. Also is a rectangle. So cm.





radius of circle cm.

Grandad

Originally Posted by Grandad

Hello thereddevilsThere's a theorem - see for instance here - that tells you that in the diagram you have here:

(It derives from the fact that the triangles and are similar. Can you see why? Hint: use angles in the same segment.)

So, if we plug in the numbers given:

cm

Now (although it doesn't look like it in your diagram) is the mid-point of (and the mid-point of ). So cm. Also is a rectangle. So cm.





radius of circle cm.

Grandad

Awesome.. Thanks !!!