ICSE Class X Math 2016 Solved Paper

In the given figure below, $A D$ is a diameter. $O$ is the centre of the circle. $A D$ is parallel to $B C$ and $∠ C B D=32^{∘}$ . Find:

Question : 9 of 57

Marks: +1, -0

∠ O B D

Solution:

Given :

{\AD} ∥{\BC}

\; ∴ \;\; ∠ {\ADB}=∠ {\DBC}=32^{∘}

\;\;\text " (alternate angles) "\;

\; {\OB}= {\OD} \;\text " (radii of the circle) "\;

\; ∴ ∠ {\OBD}=32^{∘}

(angles opposite to equal sides of a triangle)

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