 Hong Kong
Stage 4 - Stage 5

# Lengths in Circles

Lesson

We may be asked to find different values within a circle, such as an angle or a chord length. We can use all our existing mathematical knowledge, including the properties of triangles and quadrilaterals, Pythagoras' theorem, as well as congruency proofs to find certain these values.

Recap of Congruency Proofs
• SAS- two pairs of equal corresponding sides and the included angle is equal.
• AAS- two pairs equal corresponding angles, and a pair of equal corresponding sides.
• SSS- three pairs of equal corresponding sides.
• RHS- right-angled triangles, with equal hypotenuses and a pair of equal corresponding sides.

Now let's look at how we can use these geometrical principles by looking at some examples.

#### Worked Examples

##### Question 1

$C$C is the centre of the circle. Calculate $x$x, giving a reason related to the properties in a circle for your answer. ##### Question 2

What is the value of $x$x? Give reasons. ##### Question 3

Calculate $x$x, the length of a chord in the circle with centre $O$O. In your answer, give reasons related to the properties in a circle. 