Theory question 103
Linear and Simultaneous Equations(a) Solve for x and y in the following equations: 2x − y = 9/2; x + 4y = 0
(b) In the diagram, TA is a tangent to the circle at A. If BĈA = 40° and DÂT = 52°, find BÂD.
Show the model answer
Model answer
(a) From x + 4y = 0, x = −4y. Substitute: −8y − y = 9/2, so −9y = 9/2 and y = −½. Then x = 2.
(b) Angle in the alternate segment: ∠ACD = ∠DAT = 52°.
∠BCD = 40° + 52° = 92°.
ABCD is cyclic, so ∠BAD = 180° − 92° = 88°.
Explanation
Use the alternate segment theorem, then opposite angles of a cyclic quadrilateral.