Circle chord and tangent properties

Sample Circle chord and tangent properties questions

A few of the 5 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 13 marksGrade 6
   $AB$ is a chord of a circle with centre $O$ and radius $13\text{ cm}$. $AB = 24\text{ cm}$. $M$ is the midpoint of $AB$. Work out the distance $OM$. [3]
   Show the worked solution

   The line from the centre perpendicular to a chord bisects the chord, so $MB = 12\text{ cm}$. M1

   In right-angled triangle $OMB$: $OM^2 = 13^2 - 12^2 = 25$
2. Question 23 marksGrade 6
   $AB$ and $CD$ are chords of a circle with centre $O$. $AB = CD = 16\text{ cm}$
3. Question 33 marksGrade 6
   $PA$ and $PB$ are tangents from the point $P$ to a circle with centre $O$. The radius of the circle is $5\text{ cm}$ and $OP = 13\text{ cm}$
4. Question 43 marksGrade 8
   $PAB$ and $PCD$ are straight lines. The points $A$, $B$, $C$ and $D$

Common mistakes in Circle chord and tangent properties

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Adds instead of pythagoras

  Added 8 and 6. The radius is the hypotenuse of the right-angled triangle with sides 8 and 6, so use Pythagoras' theorem.

• Assumes tangent equals op

  Gave the length of OP. OP is the hypotenuse; the tangent length PA is a shorter side.

• Divides by a conversion factor where multiplying was needed

  Worked out 6 ÷ 3 or 4 ÷ 2. The intersecting chords property multiplies: AP × PB = CP × PD.