Question

3. Draw a circle of radius 3.5 cm and construct a pair of tangents to it from a point 8cm from the centre of
circle. Measure the length of the tangents
4. The perimeter of a circle with centre 'o' is 24cm. the angle formed by an arc of a
circle at its centre is 30º find the length of arc AB​

Answer 1

ANSWER:


(1) It is given that line AB is tangent to the circle at A.

∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

Thus, the measure of ∠CAB is 90º.



(2) Distance of point C from AB = 6 cm (Radius of the circle)

(3) ∆ABC is a right triangle.

CA = 6 cm and AB = 6 cm

Using Pythagoras theorem, we have

BC2=AB2+CA2⇒BC=62+62‾‾‾‾‾‾‾√ ⇒BC=62‾√ cm

Thus, d(B, C) = 62‾√
cm

(4) In right ∆ABC, AB = CA = 6 cm

∴ ∠ACB = ∠ABC (Equal sides have equal angles opposite to them)

Also, ∠ACB + ∠ABC = 90º (Using angle sum property of triangle)

∴ 2∠ABC = 90º

⇒ ∠ABC = 90°2
= 45º

Thus, the measure of ∠ABC is 45º.