Geometry · Foundation · 5 min
Tangents to circles
From a point outside a circle, two equal tangent segments meet the circle at right angles to its radii.
WHAT HAPPENS IF…With R=1.5 and OP=2.5, what is PT?
Loading the mathematical model…
At tangency, OT is perpendicular to PT. Pythagoras in triangle OTP gives PT²=OP²−R². Reflecting across OP produces the second tangent with the same length. The construction assumes OP>R.
A detail that matters
A line that cuts through the circle is a secant, not a tangent.
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