# Angle B of triangle ABC is twice the angle A. The bisector of angle B divides the AC

September 14, 2021 | education

| **Angle B of triangle ABC is twice the angle A. The bisector of angle B divides the AC side into parts AD = 6 cm and CD = 3 cm. Find the sides of the triangle ABC.**

Angle B of triangle ABC is twice the angle A. The bisector of angle B divides the AC side into parts AD = 6 cm and CD = 3 cm. Find the sides of the triangle ABC.

AC = AD + CD = 6 cm + 3 cm = 9 cm

angle b = 2 * angle a

then the Triangle ABD is isosceles since the angle b and angle a are equal

angle A is X degrees

hence BD = AD = 6 cm.

consider the triangle BCD

angle CBD = 2 * angle BСD

hence the triangles BCD and ABC are similar in three angles, then the aspect ratio is also equal to

AC / BD = BC / DC = 9/6 = BC / 3.

Hence = BC = 6 cm

AB = AC = 9 cm

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