Match the two column-Column-I-Column-IIA In the given figure- - p - 60- circll - ABCD - is a - cyclic - Quadrilateral- -1 - O - is the centre of - the - circle- 11- If -angle BOD -160- lcirc find the Measure of langle BPD-11 lend array Cbeginarray 11B - In given figure- - ABCD - is a -cyclic- q - 65- c i r c l lquadrilateral whose side AB - is a diameterll - of - the circle through A - B - C - D -11lend array

The correct option is A A s; B r; C p; D q(a) (A)→ s;(B)→ r;(C)→ p,(D)→ q (A) Consider the arc BCD of the circle. This arc makes angle ∠ BOD=160^∘ at the centr ...

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Byju's Answer

Standard IX

Mathematics

Incircle and Its Construction

Match the two...

Question

Match the two column;
$\begin{matrix} C o l u m n - I & C o l u m n - I I (A) I n t h e g i v e n f i g u r e, & (p) 60^{\circ} A B C D i s a c y c l i c Q u a d r i l a t e r a l . O i s t h e c e n t r e o f t h e c i r c l e . I f ∠ B O D = 160^{\circ} f i n d t h e M e a s u r e o f ∠ B P D . \end{matrix}$

$\begin{matrix} (B) I n g i v e n f i g u r e, A B C D i s a c y c l i c & (q) 65^{\circ} q u a d r i l a t e r a l w h o s e s i d e A B i s a d i a m e t e r o f t h e c i r c l e t h r o u g h A, B, C, D . I f ∠ A D C = 130^{\circ}, f i n d ∠ B A C . \end{matrix}$

$\begin{matrix} (C) I n t h e g i v e n f i g u r e B D = D C a n d & (r) 40^{\circ} ∠ C B D = 30^{\circ} F i n d m (∠ B A C) \end{matrix}$

$\begin{matrix} (D) I n t h e g i v e n f i g u r e, O i s t h e c e n t r e o f t h e & (s) 100^{\circ} a r c A B C s u b t e n d s a n a n g l e o f 130^{\circ} a t t h e c e n t r e . I f A B i s e x t e n d e d t o P m f i n d ∠ P B C . \end{matrix}$

Choose the correct option:

A-s; B-r; C-p; D-q

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A-s; B-p; C-q; D-r

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A-p; B-q; C-r; D-s

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A-s; B-p; C-r; D-q

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Solution

The correct option is A A-s; B-r; C-p; D-q
(a) $(A) \to s; (B) \to r; (C) \to p, (D) \to q$
(A) Consider the arc BCD of the circle. This arc makes angle $∠ B O D = 160^{\circ}$ at the centre of the circle and $∠ B A D$ at a point A on the circumference.

$∴ ∠ B A D = \frac{1}{2} ∠ B O D = 80^{\circ}$
Now, ABPD is a cyclic quadrilateral.
$\Rightarrow ∠ B A D + ∠ B P D = 180^{\circ} \Rightarrow 80^{\circ} + ∠ B P D = 180^{\circ} \Rightarrow ∠ B P D = 100^{\circ}$

(B) Since ABCD is a cyclic quadrilateral.
$∴ ∠ A D C + ∠ A B C = 180^{\circ} \Rightarrow 130^{\circ} + ∠ A B C = 180^{\circ} \Rightarrow ∠ A B C = 50^{\circ}$

Since $∠ A C B$ is the angle in a semicircle.
$∴ ∠ A C B = 90^{\circ}$
Now, in $Δ A B C$ , we have
$∠ B A C + ∠ A C B + ∠ A B C = 180^{\circ} \Rightarrow ∠ B A C = 90^{\circ} + 50^{\circ} = 180^{\circ} \Rightarrow ∠ B A C = 40^{\circ}$

(C) BD=DC
$∠ B C D = ∠ C B D = 30^{\circ}$
So, $∠ B D C = 120^{\circ}$
As ABCD is cyclic
$∴ ∠ B A C = 60^{\circ}$

(D) $∠ P B C = 65^{\circ}$ (If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite opposite angle)

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Similar questions

Match the two column;
$\begin{matrix} Column-I & Column-II (A) In the given figure, & (p) 60^{\circ} ABCD is a cyclic Quadrilateral. O is the centre of the circle. If ∠ BOD = 160^{\circ} find the Measure of ∠ BPD. \end{matrix}$

$\begin{matrix} (B) In given figure, ABCD is a cyclic & (q) 65^{\circ} quadrilateral whose side AB is a diameter of the circle through A, B, C, D. If ∠ {ADC = 130}^{\circ}, find ∠ BAC. \end{matrix}$

$\begin{matrix} (C) In the given figure BD = DC and & {(r) 40}^{\circ} ∠ {CBD = 30}^{\circ} Find m (∠ BAC) \end{matrix}$

$\begin{matrix} (D) In the given figure, O is the centre of the & {(s) 100}^{\circ} {arc ABC subtends an angle of 130}^{\circ} at the centre. If AB is extended to Pm find ∠ PBC. \end{matrix}$

Choose the correct option:

Q. In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If

∠ B O D = 160^{\circ}

, find the measure of

∠ B P D

, as shown in the given figure.

Q. Match the two columns;

\begin{matrix} C o l u m n - I & C o l u m n - I I (A) C i s a p o i n t o n t h e m i n o r a r c A B o f t h e c i r c l e w i t h c e n t r e O . & (P) 60^{\circ} G i v e n ∠ A C B = x . C a l c u l a t e ∠ x i f A C B O i s a p a r a l l e l o g r a m . (B) C h o r d E D i s p a r a l l e l t o t h e d i a m e t e r A C o f t h e c i r c l e . & (q) 120^{\circ} G i v e n ∠ C B E = 55^{\circ}, c a l c u l a t e ∠ D E C . \end{matrix}

\begin{matrix} (C) I n t h e g i v e n f i g u r e, O i s t h e c e n t r e o f t h e c i r c l e . & (r) 35^{\circ} I f ∠ A C B = 60^{\circ} f i n d ∠ O A B . \end{matrix}

\begin{matrix} (D) I n t h e g i v e n f i g u r e, O i s t h e c e n t r e o f a c i r c l e . & (s) 30^{\circ} ∠ A O B = 400 a n d ∠ B D C = 1000. F i n d ∠ O B C & . \end{matrix}

Choose the Correct option;

Match the two columns;

$\begin{matrix} Column-I & Column-II (A) C is a point on the minor arc AB of the circle with centre O. & {(P) 60}^{\circ} Given ∠ ACB = x. Calculate ∠ x if ACBO is a parallelogram. (B) Chord ED is parallel to the diameter AC of the circle. & {(q) 120}^{\circ} Given ∠ {CBE = 55}^{\circ}, calculate ∠ DEC. \end{matrix}$

$\begin{matrix} (C) In the given figure,O is the centre of the circle. & {(r) 35}^{\circ} If ∠ {ACB = 60}^{\circ} find ∠ OAB. \end{matrix}$

$\begin{matrix} (D) In the given figure, O is the centre of a circle. & {(s) 30}^{\circ} ∠ AOB = 400 and ∠ BDC = 1000. Find ∠ OBC & . \end{matrix}$

Choose the Correct option;

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