In Figure, `C\ a n d\ D` are points on the semi-circle described on `B A` as diameter. Given `m\ /_B A D=70^0\ a n d\ m\ /_D B C=30^0dot` Calculate `/_A B D\ a n d\ /_B D C`

In Figure, M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respectively. If M N=3c m ,\ N P=3. 5 c m\ a n d\ M P=2. 5 c m , calculate B C ,\ A B\ a n d\ A C

If A B , B C a n d C D are equal chords of a circle with O as centre and A D diameter, then /_A O B= 60^0 (b) 90^0 (c) 120^0 (d) none of these

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

In Fig.80, line A C l in e\ D E\ a n d\ /_A B D=32^0dot Find out the angles x\ a n d\ y\ if /_E=122^0dot

In Figure, find the four angles A ,\ B ,\ C\ a n d\ D in the parallelogram A B C D

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In Figure, A B is a diameter of the circle such that /_A=35^0a n d\ /_Q=25^0, find /_P B R

In a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m (ii) A D=5. 7 c m ,\ \ B D=9. 5 c m ,\ \ A E=3. 3 c m\ a n d\ E C=5. 5 c m .