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Circles - Higher

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Tangents from a point outside the circle are equal in length

Two tangents to a circle from a point are equal. Have a look at the line of symmetry. The two tangents fit together.

tangents

image: stage 1

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Try to work out the size of angles RPQ, SPR and PSR. Point O is the centre of the circle. The answers appear below.

image: a circle with two tangents that meet to form an angle of 50 degrees, there's a triangle in the circle with two angles marked b and c, outside the triangle an angle is marked a. s, r, u, p and q are marked at various points.

Answers:

image: a = 65 degrees because triangle QPR is isosceles, p and r are marked 65 degrees, angle q is marked 50 degrees

a=65° (this is because QPR is isosceles)

image: b = 25 degrees because angle spq is 90 degrees

b = 25° (this is because angle SPQ is 90°)

image: c = 65 degrees because triangle psr is right angled

c = 65° because triangle PSR is right-angled

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