MATHS(2) [復制鏈接]

In the figure, TA is a tangent to the circle and TC cuts the circle at B such that TB=BC, TA=4

a)Prove that triangleACT and triangleBAT are similar
b)Hence find the length of CT

a) AC is the diameter
angle ABC = 90 degrees (angle in semicircle)
TA is a tangent to the circle, so angle TAC = 90 degrees

angle ABC = angle TAC = 90 degrees
angle ATC and angle BTA (common angle)
So angle ACT = angle BAT (using angle sum of triangle, derive....)

So triangleACT and triangleBAT are similar

b) Straightforward, use corr. sides, similiar triangles in (a), ratio of te corresponding sides of the triangle is the same, get the result.

5 ming (b) part

triangleACT and triangleBAT are similar

So AT/BT=CT/AT (corr. sides, similiar triangles)

remaining parts you do it yourself

thzx