SOLUTION: I am doing a proof with no congruent or similar marks and with a circle o and it had diameter named RS, a chord named AS, a tangent named TS and a secant named TAR. And I need hel
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Question 878451: I am doing a proof with no congruent or similar marks and with a circle o and it had diameter named RS, a chord named AS, a tangent named TS and a secant named TAR. And I need help finding out why angle RAS is a right angle? Why angle RST is congruent to angle RAS? Why triangle RST is similar to triangle RAS? Why RS/RA=RT/RS? And why (RS)^2=RA times RT?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Since any tangent to a point on a circle is orthogonal to the radius at that point, angle OST, an therefore angle RST is right. Since the Inscribed Angle Theorem says that an inscribed angle is one half the measure of the same arc subtended by the central angle. A special case of this theorem (Thales Theorem) says that an angle subtended by a diameter is always right. Hence RAS is right. Since RAS is right and RAT is straight, then SAT must be right.
See if you can get where you need to go from that.
John
My calculator said it, I believe it, that settles it
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