Mathematics 4024 · O Level · Circle theorems I

Circle theorems I — practice question

A, B, C, D and E are five points lying on the circumference of a circle. $EB$ is parallel to $DC$. $\angle E\hat{A}C = 72^\circ$ and $\angle A\hat{E}B = 25^\circ$. $X$ is the point where $AC$ and $EB$ intersect.
(a(i))[1]

Find $\angle E\hat{B}C$.

(a(ii))[1]

Find $\angle C\hat{X}B$.

(a(iii))[1]

Find $\angle E\hat{D}C$.

(a(iv))[1]

Find $\angle A\hat{C}D$.

(b(i))[2]

The angle of a sector of a circle with radius $6\text{ cm}$ is $40^\circ$. Its area is $k\pi\text{ cm}^2$. Find the value of $k$.

(b(ii))[2]

Give an expression, in terms of $\pi$, for the perimeter of the sector. Write your answer in the form $(a+b\pi)$ centimetres.

(b(iii))[1]

A geometrically similar sector has perimeter $(72+n\pi)$ centimetres. Find the value of $n$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: 72

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