Junior Cycle (Ireland) · Mathematics

Plane Geometry

7 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 7 questions

In a circle with centre $O$ , the central angle $∠ A O B = 8 0^{\circ}$ . What is the inscribed angle $∠ A C B$ on the major arc?
A point $P$ is 17 units from the centre of a circle of radius 8. What is the length of a tangent from $P$ to the circle?
In a circle with centre $O$ , the central angle $∠ A O B = 7 0^{\circ}$ . What is the inscribed angle $∠ A C B$ on the major arc?
A point $P$ is 10 units from the centre of a circle of radius 6. What is the length of a tangent from $P$ to the circle?
Two angles of a triangle measure $4 7^{\circ}$ and $6 8^{\circ}$ . What is the size of the third angle?
Two parallel lines are cut by a transversal. One of the angles formed is $7 2^{\circ}$ . What is the size of the co-interior (allied) angle paired with it?
$A$ , $B$ and $C$ are points on a circle, and $[A B]$ is a diameter. If $∠ C A B = 3 5^{\circ}$ , find $∠ A B C$ .

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