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hjeffrey168
22.06.2020 •
Mathematics
How would this circle proof be set up?
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Ответ:
Step-by-step explanation:
Given: Circle O with BT as a tangent at point B.
T is the midpoint of arc CD.
To prove: (CA)(TB) = (TA)(CT)
Since point T is the midpoint of arc CD,
Therefore, m(arc CT) = m(arc TD)
and m∠CAT ≅ m∠DAT
m(∠ACT) = 90° [Angle subtended by the diameter]
By applying tangent rule in triangles ACT and ABT,
tan(∠CAT) =![\frac{CT}{CA}](/tpl/images/0691/9700/2a111.png)
Similarly, tan(∠BAT) =![\frac{TB}{TA}](/tpl/images/0691/9700/b6f31.png)
Since tan(∠CAT) = tan(∠BAT)
Therefore,![\frac{CT}{CA}=\frac{TB}{TA}](/tpl/images/0691/9700/70c2a.png)
(CA) × (TB) = (CT) × (TA)
Hence proved.
Ответ: