B, C and D are points on a circle, centre O. AB and AD are tangents to the circle.
Angle BCD=x
Find an expression for the size of angle BAD in terms of x.
Give your answer in its simplest form.
Give reasons for each stage of your working.

Step-by-step explanation:

In circle with center O,

By inscribed angle theorem:

Answer in its simplest form. = ∠BAD  = 180° -

B, C and D are points on a circle, center O.

AB and AD are tangents to the circle

We have to find an expression for the size of ∠BAD in terms of x.

∠BCD = x ( Given )

Expression for the size of ∠BAD in terms of x can be derived from the following steps

Center angle is twice the angle inscribed at the arc of a circle .

∠BCD =(1/2) ∠ BOD

(1/2) ∠ BOD

= ∠ BOD ........ (1)

So in quadrilateral BODA

∠BOD + ∠ BAD  = 180° ........(2)  ( By two tangent theorem)

Since ∠ ODA = 90 °

         ∠ OBD = 90 °

From Equation (1) and (2)

∠BAD  = 180° -

Answer in its simplest form is  given by the expression given as follows ∠BAD  = 180° -

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80 the answer is 80

step-by-step explanation:

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: