Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

The diagram depicts a circle with centre $O$, and points $B$ and $D$ lie on the circumference. Line $AC$ is tangent to the circle at $B$. $OB$ is parallel to $DC$, and angle $OAB = 49^\circ$.
(a(i))[1]

State the mathematical name of line $OB$.

(a(ii))[1]

State the reason why angle $ABO$ is $90^\circ$.

(a(iii))[1]

Find angle $AOB$.

(a(iv))[1]

State the reason why angle $ADC$ = angle $AOB$.

(a(v))[1]

Complete the statement by inserting a mathematical word. Triangle $AOB$ is [BLANK] to triangle $ADC$.

(a(vi))[6]

Calculate the values of $OB$, $OA$ and the area of triangle $AOB$.

(b)[1]

Show that the interior-angle sum of this polygon equals $900^\circ$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The radius

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI