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Standard IX

Mathematics

Incircle and Its Construction

Seg AB is t...

Question

Seg $A B$ is the diameter of a circle. $C$ is the point on the circumference such that in $△ A B C$ , $∠ B$ is less by $10^{o}$ than $∠ A$ . Find the measures of all angles of $△ A B C$ .

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Solution

Angle subtended by diameter on any point on circle is $90^{o}$
$\Rightarrow ∠ A C B = 90^{o}$
In $△ A B C, ∠ B + ∠ C + 90 = 180$
$\Rightarrow ∠ A - 10 + ∠ A + 90 = 180 \Rightarrow ∠ A = 50^{o}$
$\Rightarrow ∠ B = 40^{o}$

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Seg AB is the diameter of a circle. C is the point on the circumference such that in △ABC, ∠B is less by 10o than ∠A. Find the measures of all angles of △ABC.

Angle subtended by diameter on any point on circle is 90o ⇒∠ACB=90o In △ABC,∠B+∠C+90=180⇒∠A−10+∠A+90=180⇒∠A=50o⇒∠B=40o

Seg $A B$ is the diameter of a circle. $C$ is the point on the circumference such that in $△ A B C$ , $∠ B$ is less by $10^{o}$ than $∠ A$ . Find the measures of all angles of $△ A B C$ .

Angle subtended by diameter on any point on circle is $90^{o}$
$\Rightarrow ∠ A C B = 90^{o}$
In $△ A B C, ∠ B + ∠ C + 90 = 180$
$\Rightarrow ∠ A - 10 + ∠ A + 90 = 180 \Rightarrow ∠ A = 50^{o}$
$\Rightarrow ∠ B = 40^{o}$