Any triangle where two of the sides are radii of the same circle must be isosceles.
isos tri = radii, angle sum = 180
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When an angle is drawn from the ends of an arc to the centre of a circle, it is twice the size of an angle drawn from the ends of the same arc to any point on the opposite circumference of the circle.
Angle @ centre = 2 x angle at circumference
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When the arc forms a semi-circle, any angle on the circumference is a right angle
angle semi-circle = 90
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Angles extending to the circumference from the same arc are equal
angles on same arc =
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On a cyclic quad, opposite angles are supplementry
cyc quad, opp angles add up to 180
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On a cyclic quad, each opposite angle is equal to the interior opposite angle
cyc quad, ext angle = int opp angle
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When a tangent is drawn to a circle, it makes a right angle with the radius at the point of contact
tgt right angle rad
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the angle between a chord and a tangent equals the angle in the opposite segment
angle between tgt and chord = angle on chord in opp segment
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Other cards in this set
Card 2
Front
Angle @ centre = 2 x angle at circumference
Back
When an angle is drawn from the ends of an arc to the centre of a circle, it is twice the size of an angle drawn from the ends of the same arc to any point on the opposite circumference of the circle.
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