Question

In figure l and m are two parallel tangents at c makes an intercept DE between the tangent l and m prove that

Answer 1

Answer:

Hence we prove that Angle DFE is 90 Degree

Step-by-step explanation:

In triangles ADF and DFC, we have DA = DC ..(Tangents drawn from external point are equal in length)

DF = DF  ..(Common)

AF = CF  ..(Radii of the same circle)

So, by SSS-Criterion of congruence, we get

▲ ADF = ▲ DFC

= <ADF = <CDF

= <ADC = 2<CDF

..(i)

Similarly, we can prove that

<BEF = <CEF

= <CEB = 2<CEF

...(ii)

Now, <ADC + <CEB = 180 ...(Sum of the interior angles on the same side of transversal is 180)

- 2(<CDF + <CDF) = 180  

= CDF + CEF = 90

Now, in ZDEF,

= <DFE + <CDF + <CEF = 180

= <DFE + 90 = 180

= <DFE = 180 - 90