Question

Diameter AB is produced to C. CE is a tangent to the

circle at E. AE is produced to D and DC LAC.
a) Prove that:
(i) BEDC is a cyclic quadrilateral
(ii) D₁ = Â
(iii) CE = CD
(iv) B1= B3
b) Why can DB not be a tangent to the circle through BAE?

Answer 1

Hi,

Explanation:

i)

BEDC having 2 right opposed angles , their sum is 180° so, is a cyclic quadrilateral.

II)

∠EAB and ∠BEC are equal (intercept the same arc EB)

∠EDC and ∠BEC are equal (intercept the same arc BC)

so ∠A and ∠D1 are equal

III)

triangles ECG and CDB are equal : they are right and have on angle equal => CE=CD

IV)

complement of A is B1

complement of D1 is B3

since ∠A =∠D1 their complement are equal.

Answer 2

BE II CD so the arc BD is equal to the arc of B^x=^E BDIIUD