Learning Resources

Investigation 5: Tangent Properties

Test yourself (Answers)

1. In the diagram below, AB is a tangent at C and XC is a diameter.
mÐ YCB = 58° and mÐ XYZ = 38°.

Find the following:
mÐ YXC, mÐ YZC, mÐ YCX, mÐ ZCA, mÐ ZCX, mÐ ZYC,

mÐ YXC = 58° (inscribed angle on opposite side of chord CY from the tangent chord angle, Ð YCB)

mÐ YZC = 58° (same as above)

mÐ YCX = 90° - 58° = 32° (tangent perpendicular to radius)

mÐ ZYC = 90° - 38° = 52° (Inscribed angle in a semicircle is a right angle)

mÐ ZCA = mÐ ZYC = 52 (tangent chord angle is equal to inscribed angle on the opposite side of the chord. )

mÐ ZCX = mÐ XYZ = 38° (inscribed angles intercepting the same arc are equal.)