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Let be a diameter of a circle centered at . Let be a point on the circle, and let the tangent at intersect the tangent at and at and , respectively. If , find , in degrees.

Respuesta :

The degrees of the angle is : = 47

What is Circle and tangent?

An perfect one-point touch on a circle without ever going inside of it is what is meant by a line being a tangent to it. The topic of multiple theorems, tangent lines to circles are crucial to numerous geometrical structures and proofs.

According to the given information:

Angle BAE  = 43°   ...so   minor  arc BE  will = 86°

And angle CBE  = 1/2 of this arc  = 43°

since,

CB and  CE  are tangents  to  the circle from a common point C

they are equal.

Thus...

in triangle BCE....BC  = EC.

the angles opposite these sides are also equal

So,

angle CBE  = angle BEC

triangle AEB

angle AEB  intercepts a diameter

so,

its measure   = 90°

angle AEB  + angle BEC  + angle CED  = 180°

90   +   43   +   angle CED   = 180

133 + angle  CED  = 180    

subtract   133 from each side.

angle CED  =  47°

The degrees of the angle is : = 47

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