Question

(2y + 6) 40"
26. In the adjoining figure, show that AABC = ADBC.
Hence, find the values of x and y.
B
56°
12.
27. By using ruler and compasses only, construct a triangle ABC with
= 60° and ZA = 90°.​

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=6√2  cm

Thus, d(B, C) = 6√2 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