# Geometry help: right triangle inscribed in a circle with a tangent and angle bisector?

A right triangle ABC with right angle at B is inscribed in a circle and a tangent to the

circle is drawn at A. The bisector of angle ACB meets A.B at D and the tangent at E. Prove

that angle AED equals angle ADE. [

### 3 Answers

- SamwiseLv 77 years agoFavorite Answer
I had to draw myself a picture to see this:

AC is a diameter of the circle [hypotenuse of an inscribed right triangle]

AE is perpendicular to AC [tangent to, and diameter of, the circle]

Angle CAE is a right angle [definition of perpendicular]

Angle CBD is a right angle [given]

Angles ACE and BCD are congruent [bisection of angle ACB]

Triangles AEC and BDC are similar [angle-angle similarity]

Angle AEC equals angle BDC [corresponding angles of similar triangles]

Angle AED equals angle AEC [same angle]

Angle BDC equals angle ADE [vertical angles]

Angle AED equals angle ADE [transitive property of equality]

- neuhausLv 43 years ago
a million. F 2. F 3. F 4. T 5. T 6. F, not a rectangle, a minimum of not in my e book 7. F, tangent is a line on exterior edge of the it is perpendicular to the radius 8. ? lacking term: a million, 4, 9, sixteen, 25, 36 (you upload the subsequent ordinary quantity, the 1st time you upload 3, then 5, 7, 9, 11, ect.) an acute triangle has attitude measures that are all below ninety levels diameter is a chord passing by using center of circle degree of attitude 2 is a hundred and eighty-sixty 4=116