virtus
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virtus
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dw:1345271219374:dw

virtus
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prove that triangle OTM is similar to triangle TPM

mukushla
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dw:1345271392740:dw

dpaInc
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since both are right triangles and <TOM is congruent to <TOP, those two triangles are similar by AAA

dpaInc
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^^^ that is assuming PT is tangent to the circle....

virtus
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Yes PT is a tangent to the circle, but can you elaborate on why it is similar by AAA. i don't get it thanks

mukushla
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PT is a tangent to the circle so OT is perpendicular to PT and PTO=90 is that right?

rsadhvika
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both are right triangles and one angle O is common

rsadhvika
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dw:1345271947198:dw

virtus
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umm we are proving OTM is similar to triangle TPM

virtus
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not OTM is similar to triangle OTP

rsadhvika
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first step we are proving OTM ~ OPT
next we gona prove OPT ~ TPM
and conclude OTM ~ TPM

rsadhvika
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did you understand why OTM ~ OPT ?

rsadhvika
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dw:1345272356748:dw

rsadhvika
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dw:1345272694033:dw

rsadhvika
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its just a simple game with \(\alpha\) , \(90\alpha\), and seeing which triangles have same set of angles

virtus
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ohhh sorry @rsadhvika i understand thanks!

rsadhvika
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okay no problem =))