Question

L and m are two parallel tangents at a and

b. the tangent at c makes an intercept de between l and m. prove that ∠dfe = 90°.

Answer 1

Given:  l and m are two parallel tangents at A and B. The tangent at C makes an intercept DE between l and m.

To Prove: ∠DFE=90°

Construction: Join AF,FB,FC

Proof: 

In triangles ADF and DFC,

DA = DC[ Tangents drawn from an external point are equal in length]

DF = DF [Common]

AF = CF [Radii of the same circle]

∴ΔADF is congruent to ΔCDF [By SSS congruence]

⇒∠ADF = ∠CDF