Question

i. Find the length of BC

a. 4√5 b.5√6 c.10 d.6√5

ii. Find <BAC, If <ABC=30֯

a.60֯ b.120֯ c.90֯ d.45֯

iii. Relation between BC and BD

Answer 1

Answer:

i) a)4√5

ii) a)60°

iii) BC=BD

Step-by-step explanation:

In ∆ ABC, Angle A is 90° because tangent through a point on a circle is perpendicular to the radius through point of contact.

i)

So by Pythagoras Theorem,

AB^2= AC^2 + BC^2

12^2= 8^2 + BC^2

144-64=BC^2

BC=√80= 4√5

So option (a)4√5 is correct

ii)

By Angle Sum Property, in ∆ ABC

/_A + /_ B + /_ C= 180°

/_A + 30° + 90°= 180°

/_A= 180°-120°

/_A= 60°

So option (a)60° is correct

iii) As BC and BD are tangents from a point B so they are equal.

Hope it helps ☺️