3 years ago

A tangent to a circle passes through the center of the circleTruefalsesometimes true

Mathematics

1 answer:

liberstina [14]3 years ago

8 0

Answer:

False.

Step-by-step explanation:

A tangent is a line that only touches exactly one point of the circle. (The outer edge) :)

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Please help me to prove this.

Vanyuwa [196]

<h3><u>Answer</u> :</h3>

For triangle : A + B + C = π

⇒ A + B = π - C

⇒ cot(A + B) = cot(π - C)

⇒ $\sf\dfrac{cotA\:cotB-1}{cotB+cotA}=-cotA$

⇒ $\bf{cotA\:cotB+cotB\:cotC+cotC\:cotA=1}$

<u>Now 1st part of the given expression</u>!

⇒ $\sf\dfrac{cosA}{sinB\:sinC}$

⇒ $\sf\dfrac{cos(\pi-(B+C))}{sinB\:sinC}$

⇒ $\sf\dfrac{-cosB\:cosC+sinB\:sinC}{sinB\:sinC}$

⇒ 1 - cotB cotC

<u>Similarly 2nd part</u>!

⇒ 1 - cotA cotB

<u>Similarly 3rd part</u>!

⇒ 1 - cotC cotA

<u>LHS</u> :

$\circ\:\sf{3-(cotA\:cotB+cotB\:cotC+cotC\:cotA)}$

$\circ\:\sf{3-1}$

$\circ\:\bf{2}$ = <u>RHS</u>

<h3>Hence Proved!!</h3>

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Answer:

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Step-by-step explanation:

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A tangent to a circle passes through the center of the circleTruefalsesometimes true​

A tangent to a circle passes through the center of the circleTruefalsesometimes true