Question

Q9) IN FIGURE 10.13,XY AND X'Y' ARE 2 PARALLEL TANGENTS TO A CIRCLE WITH CENTER O AND ANOTHER TANGENT AB WITH POINT OF CONTACT c INTERSECTING XY at a AND X'Y'AT B.PROVE THAT

Answer 1

Tangent drawn from a external point to a circle
There fore AP= AC
In ∆PAO and ∆AOC
We have AP = AC. ( tangents )
OA = OA ( common)
PO = OC. ( radii of the same circle )
Angle PAO = Angle CAO ( CPCT)
Similarly , we can prove that
Angle QBO = Angle CBO
Angle CBO = 2angle CBQ
Angle PAC + Angle CBO = 180


2angle CAO + 2angle CBO = 180 2angle ( CAO + CBO ) = 180
Angle CAO + CBO = 180÷2

CAO + CBO = 90°

Angle AOB = 90°

Answer 2

Hope u understand and it help u friend...!!!!