In the adjoining figure, A B and C D are diameter of a circle with centre O . If &ang; OBD = 35 ° , then find the value of x .

Consider the given figure We know that the angles at the circumference subtended by the same arc are equal. ⇒ ∠ A C D = ∠ A B D = 35 ° Now, in △ O A C , we have O A = O C (radii of the circle) ⇒ ∠ A C D = x = 35 ° (Angles opposite to two equal sides of a triangle are equal). Hence, x = 35 °

In the adjoining figure, A B and C D are diameter of a circle with centre O . If &ang; OBD = 35 ° , then find the value of x .

Consider the given figure We know that the angles at the circumference subtended by the same arc are equal. ⇒ ∠ A C D = ∠ A B D = 35 ° Now, in △ O A C , we have O A = O C (radii of the circle) ⇒ ∠ A C D = x = 35 ° (Angles opposite to two equal sides of a triangle are equal). Hence, x = 35 °

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 10 - Circles>Very Short Answer Questions>Q 8

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In the adjoining figure, $A B$ and $C D$ are diameter of a circle with centre $O$ . If $∠ OBD = 35 °$ , then find the value of $x$ .

Important Questions on Circles

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 10 - Circles>Very Short Answer Questions>Q 9

In the adjoining figure, $A B C D$ is a cyclic quadrilateral. If the angles are as given in the figure, then find the values of $x$ and $y$ .

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 10 - Circles>Very Short Answer Questions>Q 10

In the adjoining figure, $A B C D$ is a cyclic quadrilateral in which $A B | | D C$ . If $∠ A = 80 °$ , then find $∠ B$ .

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CBSE Syllabus Standard Mathematics for Class IX>Chapter 10 - Circles>Very Short Answer Questions>Q 11

Two congruent circles intersect at points $P$ and $Q$ . A line through $P$ and perpendicular to $P Q$ meets the circles at $A$ and $B$ . Show that $A Q = B Q$ .