coordinate geometry: circles - AB is a diameter of a circle, center O. C is a point on the circumference of the circle, such that ∠CAB = 2 × ∠CBA What is the size of ∠CBA?

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Recall all the theorems of the circle.

Step 2: Note down given values and examine the figure

Step 3: Identify the suitable theorem for the given question.

NOTE: An angle inscribed in a semicircle is always a right angle.

EXAMPLE: In triangle ABC \angle C=90\degree

Step 4: Find the two remaining angles.

NOTE: The sum of the three interior angles is equal to 180.

EXAMPLE: From triangle ABC

\angle A+\angle B+\angle C=180\degree

\angle A\degree+\angle B+90\degree=180

∠A+∠B=90

Step 5: Understand the hint given in the question to find the unknown angles.

EXAMPLE: HINT: ∠\ CAB\ =\ 2\ \cdot∠CBA\ or \angle A = 2 * \angle B

So, \angle A + 2 * \angle A = 90

, 3 * \angle A = 90

\angle A = 30\degree