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19/07/2021 1:26 pm
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ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
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19/07/2021 1:28 pm
We know that AC is the common hypotenuse and ∠B = ∠D = 90°.
Now, it has to be proven that ∠CAD = ∠CBD
Since, ∠ABC and ∠ADC are 90°, it can be said that They lie in the semi-circle.
So, triangles ABC and ADC are in the semi-circle and the points A, B, C and D are concyclic.
Hence, CD is the chord of the circle with center O.
We know that the angles which are in the same segment of the circle are equal.
∴ ∠CAD = ∠CBD