Question

the radius of the circle with centre c is 6cm line ab is tangent what is the measure of <cab ?​

Answer 1

Step-by-step explanation:

Answer

Join A,C and B,C

( 1 ) We have the theorem,

A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

∴∠CAB=90

∘

( 2 ) The distance of point C from the line AB is equal to the radius of the circle. ie., line AC

AC=radius of circle=6 cm

( 3 ) AB=6 cm and AC=6 cm

ABC is a right angles triangle.

By Pythagoras theorem,

BC

2

=AB

2

+AC

2

BC

2

=6

2

+6

2

=36+36

BC=

72

=6

2

cm

∴ d(B, C)=6

2

cm

( 4 ) ABC is an isosceles triangle.

AB=AC

⟹∠ABC=∠ACB ------ Angles opposite to equal sides in a triangle are equal

In △ABC,

∠BAC+∠ABC+∠ACB=180

∘

90

∘

+2∠ABC=180

∘

2∠ABC=180

∘

−90

∘

=90

∘

∴∠ABC=

2

90

∘

=45

∘