Mathematics 4024 · O Level · Circle theorems I

Circle theorems I — practice question

In the circle with centre $O$, $AC$ is a diameter. $BCD$ and $OED$ are straight lines. $AC = 6\text{ cm}$ and $CD = 3\text{ cm}$. $\angle BAC = 34^{\circ}$.
(a(i))[1]

Explain why the value of $\angle BCA$ is $56^{\circ}$.

(a(ii))[2]

Find the value of $\angle COD$.

(a(iii))[1]

Find the value of $\angle OCE$.

(b(i))[2]

Explain why $PT$ is equal to $PR$.

(b(ii))[3]

This figure is a section of the larger diagram above. $PQ = 12\text{ cm}$, $PR = 5\text{ cm}$ and $QR = 8.5\text{ cm}$. It is given that $\frac{PQ}{PR} = \frac{QS}{SR}$. Find $SR$.

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