Answer:
* AD is congruent to DC and BD true
* m∠B = 90° true
* The measure of arc AC is equal to the measure of arc AB not be true ( The right answer )
* The measure of arc AB is equal to measure of arc BC true
Explanation:
∵ D is the center of the circle and A , B and C are points on the circle
∴ AD , DB and DC are radii on the circle D
∴ AD ≡ DC ≡ DB
∵ AC passing through point D which is the center of the circle
∴ AC is the diameter of the circle D
∵ ∠B is opposite to the diameter of the circle and vertex B lies on the circle
∵ ∠B is an inscribed angle and ∠ADC is a central angle subtended by the same arc AC
∴m∠B = half m∠ADC
∵ m∠ADC = 180°
∴ m∠B = 90°
∵ The measure of arc AC = 180°
∵ ΔABC is isosceles and m∠B = 90°
∴ m∠BAC = m∠BCA = (180° - 90°) ÷ 2 = 45°
∵ ∠ACB is an inscribed angle subtended by arc AB
∴ m∠ACB = half measure of arc AB
∵ The measure of arc AB = 45° × 2 = 90°
∴ The measure of arc AC ≠ the measure of arc AB
∵ Δ ABC is an isosceles triangle and m∠B = 90°
∴ AB = BC
∵ AB subtended by arc AB
∵ BC subtended by arc BC
∴ The length of arc AB = the length of arc BC
∵ If two arcs are equal in length, then they will be equal in measure
∴ The measure of arc AB is equal to the measure of arc BC