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Answer:
Explanation:
1)- It is given that line AB is tangent to the circle at A.
∴∠CAB=90
o
(Tangent at any point of a circle is perpendicular to the radius throught the point of contact)
Thus, the measure of ∠CAB is 90
o
.2)- Distance of point C from AB=6cm (Radius of the circle)
3)- △ABC is a right triangle.
CA=6cm and AB=6cm
Using Pythagoras theorem, we have
BC
2
=AB
2
+CA
2
⇒BC=
6
2
+6
2
⇒BC=6
2
cm
thus, d(B,C)=6
2
cm
4)- n right △ABC, AB=CA=6cm
∴∠ACB=∠ABC (Equal sides have equal angles opposite to them)
Also,∠ACB+∠ABC=90
o
(Using angle sum property of triangle)
∴2∠ABC=90
o
⇒∠ABC=
2
90
o
Thus, the measure of ∠ABC is 45
o
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