Question

A, B, C, and D are points on the circumference of a circle, center O. ED is a tangent to the circle. Angle ODB = 25°. Work out angle BAD. You must give a reason for each stage of your working.

a) (55^circ); Angle at the center is twice the angle at the circumference.

b) (110^circ); Tangent and radius are perpendicular.

c) (70^circ); Exterior angle of a triangle is equal to the sum of its interior opposite angles.

d) (35^circ); Alternate angles between parallel lines are equal.

Answer 1

To find angle BAD, we first note that angle ODB is given as 25°. Since angle ODB is subtended by an arc that is twice the length of arc AB, we can find the measure of arc AB by multiplying 25° by 2, giving us 50°. Now, using the fact that a tangent line is perpendicular to the radius, we can deduce that angle AOB is 90°. Finally, using the fact that the sum of the angles in a triangle is 180°, we can find angle BAD by subtracting the known angles from 180°. Thus, angle BAD is 180° - 50° - 90° = 40°.

Step-by-step explanation:

To find angle BAD, we first note that angle ODB is given as 25°. Since angle ODB is subtended by an arc that is twice the length of arc AB, we can find the measure of arc AB by multiplying 25° by 2, giving us 50°. Now, using the fact that a tangent line is perpendicular to the radius, we can deduce that angle AOB is 90°. Finally, using the fact that the sum of the angles in a triangle is 180°, we can find angle BAD by subtracting the known angles from 180°. Thus, angle BAD is 180° - 50° - 90° = 40°.