Question

in the figure the radius of the circle is 6cm angle AB=AC angle B=70​

Answer 1

Answer:

a) ∠A = 40°

b) BC = 4.08 cm

Step-by-step explanation:

a) Given AB = AC

angles opposite to congruent sides are equal.

∴ ∠B = ∠C = 70°

Sum of angles in Δ = 180°

∠A + ∠B + ∠C = 180°

                 ∠A = 180° - ∠B - ∠C

                 ∠A = 180 -70 - 70

                 ∠A = 40°

b) Length of BC

Let the centre of the circle be O.

Join OB and construct OM ⊥ BC.

In ΔOBM,

cos 70° = $\frac{BM}{BO}$

but BO = 6 (radius)

∴ BM = cos 70° x BO

         = 0.34 x 6

         = 2.04

BC = BM + MC

but BM = MC as ⊥ drawn from centre to the chord divides the chord in equal parts

∴ BC = 2.04 + 2.04

        = 4.08 cm