Prove intercept of a tangent between two parallel, Mathematics

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

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Since Δ ADF ≅ Δ DFC

∠ADF = ∠CDF

∴ ∠ADC = 2 ∠CDF

Similarly we can prove ∠CEB = 2∠CEF

Since  || m

∠ADC + ∠CEB = 180o

⇒2∠CDF + 2∠CEF = 180o

⇒ ∠CDF + ∠CEF = 90o

In Δ DFE

∠DFE = 90o

Posted Date: 4/10/2013 5:27:43 AM | Location : United States






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