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P is a point on the side B C of a tr...

`P` is a point on the side `B C` of a triangle `A B C` such that `A B=A P`. Through `A\ a n d\ C ,\ ` lines are drawn parallel to `B C\ a n d\ P A ,` respectively, so as to intersect at `D` as shown in Figure. Show that `A B C D` is a cyclic quadrilateral.

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P is a point on the side B C of a triangle A B C such that A B=A Pdot Through A and C, lines are drawn parallel to B C and P A , respectively, so as to intersect at D as shown in Figure. Show that A B C D is a cyclic quadrilateral.

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l\ a n d\ m are two parallel lines intersected by another pair of parallel lines p\ a n d\ q as shown in figure. Show that A B C~= C D A

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .

In Figure, A B\ a n d\ C D are two chords of a circle, intersecting each other at P such that A P=C P . Show that A B=C D .

Given /_\A B C , lines are drawn through A ,\ B\ a n d\ C parallel respectively to the sides B C ,\ C A\ a n d\ A B ,\ forming /_\P Q R. (F igu r e) . Show that B C=1/2Q R .

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

Given A B C , lines are drawn through A ,\ B\ a n d\ C parallel respectively to the sides B C ,\ C A\ a n d\ A B ,\ forming triangle P Q R . Show that BC=1/2QR.

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

In figure, A B\ a n d\ C D are straight lines and O P\ a n d\ O Q are respectively the bisectors of angles /_B O D\ a n d\ /_A O C . Show that the rays O P\ a n d\ O Q are in the same line.

RD SHARMA ENGLISH-CIRCLE -All Questions
  1. P Q\ a n d\ R S are two parallel chords of a circle and lines R P\ ...

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  2. A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D in...

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  3. P is a point on the side B C of a triangle A B C such that A B=A P...

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  4. A B C is a triangle in which A B=A C\ a n d\ P is a point on A C ....

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  5. In any triangle ABC, if the angle bisector of /A and perpendicular bi...

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  6. Let the vertex of an angle ABC be located outside a circle and let t...

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  7. In Figure, A B C is an equilateral triangle. Find m\ /B E C

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  8. In Figure, O is the centre of the circle. If /B O D=160^@, find the ...

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  9. In Figure A B C D is a cyclic quadrilateral. If /B C D=100^0a n d\ /A ...

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  10. If A B C D is a cyclic quadrilateral in which A D || B C . Prove tha...

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  11. In Figure, O is the centre of the circle. Find /C B D

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  12. A B\ a n d\ C D are diameters of a circle with centre Odot If /O B D...

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  13. On a semi-circle with A B as diameter, a point C is taken, so...

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  14. In a cyclic quadrilateral A B C D, if AB || CD\ a n d\ /B=70^0, find...

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  15. In a cyclic quadrilateral A B C D , if /A=3 /C. Find /A

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  16. In Figure, O is the centre of the circle and /D A B=50^0dot Calcula...

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  17. In Figure, if /B A C=60^0\ a n d\ /B C A=20^0,\ find /A D C

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  18. In Figure, if A B C is an equilateral triangle. Find /B D C\ a n d\...

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  19. In Figure, O is the centre of the circle. If /C E A=30^0, find the ...

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  20. In Figure, /B A D=78^0,\ /D C F=x^0a n d\ /D E F=y^0dot Find the va...

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