The fig. 3.13 shows, a semi circle drawn with diameter AC and centre D. Show that $∠$ ABC is right angle.

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Solution

$In the figure, we can see that DA = DB = DC (radii of the circle) In △ ABD, l et ∠ DAB = ∠ ABD = x (∵ AD = BD) In △ DBC, l et ∠ DBC = ∠ DCB = y (∵ DC = BD) In △ ABC, x + y + x + y = 180 ° \Rightarrow 2 x + 2 y = 180 ° \Rightarrow x + y = 90 ° Thus, ∠ B = 90 ° . Then, ∠ ABC = 90 ° . Thus, ∠ ABC is a right angle .$

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The fig. 3.13 shows, a semi circle drawn with diameter AC and centre D. Show that ∠ABC is right angle.

In the figure, we can see thatDA = DB = DC (radii of the circle)In △ABD,let ∠DAB = ∠ABD =x (∵ AD = BD)In △DBC,let ∠DBC = ∠DCB = y (∵DC=BD)In △ABC,x+y+x+y = 180°⇒2x+2y = 180°⇒x+y =90°Thus, ∠B = 90°. Then, ∠ABC = 90°.Thus, ∠ABC is a right angle.

The fig. 3.13 shows, a semi circle drawn with diameter AC and centre D. Show that $∠$ ABC is right angle.