In a circle, chords $AB$ and $CD$ intersect at point $E$ inside the circle. The segment lengths are $AE=4$, $EB=6$, $CE=3$. The distance from the centre $O$ of the circle to the intersection point $E$ is $5$ units.

(i) Find the radius of the circle.
(ii) Determine the perpendicular distance from the centre $O$ to chord $AB$.
(iii) Compute the area of triangle $OAB$ (express your answer in simplest radical form).

Question

In a circle, chords $AB$ and $CD$ intersect at point $E$ inside the circle. The segment lengths are $AE=4$, $EB=6$, $CE=3$. The distance from the centre $O$ of the circle to the intersection point $E$ is $5$ units.

(i) Find the radius of the circle.
(ii) Determine the perpendicular distance from the centre $O$ to chord $AB$.
(iii) Compute the area of triangle $OAB$ (express your answer in simplest radical form).

Accepted Answer

(i) radius = 7 units; (ii) distance = 2\sqrt{6} units; (iii) area = 10\sqrt{6} square units

Neco Model Questions Vol1 2025 Mathematics Question 50

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