Theorems (Leaving Cert Mathematics): Quizzes

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Circle Theorems
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What equals the product AP×PBAP \times PB when chords ABAB and CDCD intersect at PP inside a circle?

CP×PDCP \times PD

Two chords intersect at PP. If AP=4AP = 4, PB=6PB = 6, and CP=3CP = 3, find PDPD.

88

Why does the Intersecting Chords Theorem work?

Similarity of triangles formed

What angle does a diameter subtend at the circumference of a circle?

90∘90^\circ

A triangle is inscribed in a circle with the diameter as one side. What type is it?

Right triangle

What is true about opposite angles in a cyclic quadrilateral?

They are supplementary

In a cyclic quadrilateral, one angle is 110∘110^\circ. What is the opposite angle?

70∘70^\circ

How is a tangent related to the radius at the point of contact?

Perpendicular to it

What is ∠OAB\angle OAB where OAOA is a radius and ABAB is a tangent at AA?

90∘90^\circ

What equals the angle between a tangent and chord at the point of contact?

Angle in alternate segment

A tangent meets chord PQPQ at PP with angle 50∘50^\circ. What is the alternate segment angle?

50∘50^\circ

Why are opposite angles in a cyclic quadrilateral supplementary?

Arcs form full circle 360∘360^\circ

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