Question

From the adjoining figure, if radius of the circle

with centre C is 5cm, find the distance of the

tangent from point C..​

Answer 1

$\huge\underline\mathrm\orange{Answer}$

(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) In 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°

⇒∠ABC= 2/90°

Thus, the measure of ∠ABC is 45°