In the figure, $TA$ and $TB$ are tangents to the circle, centre $O$, from $T$. Given that&nb

Question

In the figure, $TA$ and $TB$ are tangents to the circle, centre $O$, from $T$. Given that $AOC$ is a diameter of the circle, state a reason why $\angle AOB=2\angle ACB$. Hence, prove that $CB$ is parallel to $OT$, A circle with diameter $OT$ can be drawn to pass through $A$ and $B$, $\Delta OBC$ is similar to $\Delta TAB$.

Accepted Answer

(i) The angle at the centre is twice the angle at the circumference (ii) Proved: $CB\parallel OT$ (iii) Proved: the circle with diameter $OT$ passes through $A$ and $B$ (iv) Proved: $\triangle OBC\sim\triangle TAB$

Proofs in Plane Geometry - Similarity

Proofs in Plane Geometry - Similarity

Video Solution:

Solution:

Solution locked