Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

Points A, B and C lie on the circumference of the circle, with centre O. The straight line DE is in contact with the circle at B. The diagram gives angle at A as 35^{\circ}.
(a)[1]

State the mathematical name for the line DE.

(b)[1]

Sketch a radius on the circle.

(c(i))[2]

Complete the statements below. Angle $ABD$ = ............ because ........................................................

(c(ii))[2]

Complete the statements below. Angle $ACB$ = ............ because ........................................................

(d(i))[3]

Calculate the area of the circle. Include the units in your answer.

(d(ii))[2]

Calculate the value of $BC$.

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