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Question

In the diagram given below $$\angle EDC$$. The tangent drawn to the circle at $$C$$ makes an angle of $${50}^{o}$$ with $$AB$$ produced. Find the measure of $$\angle ACB$$.
1271905_40fe00c5eeb64de1bca333da3a7d9311.png


Solution

$$\angle{AGE}={50}^{\circ}$$
Consider $$AC$$ diameter
In $$\triangle{ACG},\angle{ACG}={90}^{\circ}$$
$$\Rightarrow \angle{CAG}={40}^{\circ}$$ $$(sum~ of ~angle ~in ~triangle)$$
In $$\triangle{ACB},\angle{CAB}={40}^{\circ}$$
$$\Rightarrow \angle{ACB}={50}^{\circ}$$

Mathematics

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