21.3 Tangents and chords — Practise

Work independently. Questions become more demanding as you progress. Check your answers after you have attempted the set.

1. H A tangent touches a circle at $T$. What angle does the radius to $T$ make with the tangent?
2. H Tangents from $P$ touch a circle at $A$ and $B$. If $PA=8.3$ cm, find $PB$.
3. H A perpendicular from the centre meets a chord of length $14$ cm. Find each half.
4. H The angle between a tangent and chord is $53^\circ$. Find the angle in the alternate segment.
5. H At a point of contact, the angle between a radius and tangent is $90^\circ$. Another angle in the triangle is $32^\circ$. Find the third angle.
6. H A perpendicular from the centre bisects a chord. One half is $6.8$ cm. Find the full chord length.
7. H Two tangents from one point have lengths $(2x+1)$ cm and $13$ cm. Find $x$.
8. H The alternate segment angle is $(3x-4)^\circ$. The tangent-chord angle is $50^\circ$. Find $x$.
9. H A perpendicular from the centre bisects a chord. The two pieces are $(x+2)$ cm and $(3x-6)$ cm. Find $x$.
10. H A tangent-chord angle is $42^\circ$. The angle at the centre standing on the corresponding arc is twice the angle in the alternate segment. Find the centre angle.