Q In a square ABCD m diagonals meet at O P is a point on BC, such that - Maths - Rectilinear Figures

Question

Q In a square ABCD m diagonals meet at O P is a point on BC, such
that OB = BP
Show that :
(i) ∠ P O C   =   22 1 2 °
(ii) ∠ B D C   =   2   ∠ P O C
(iii) ∠ B O P   =   3   ∠ C O P

Neha Sethi · Accepted Answer

Dear student
<img src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4123606/2013_10_26_09_36_36/pic8%20png">
To prove:i) ∠POC=2212°Given: ABCD is  a square and OB=BP⇒∠BOP=∠BPO  
1 angles opposite to equal sides are equalAlso, ∠OBP=90°2=45° 
2  By symmteryConsider △OBP  by angle sum property⇒∠BOP+∠BPO+∠OBP=180°   ⇒2∠BOP+45°=180°  using 1 and 2⇒2∠BOP=135°⇒∠BOP=67
5°  
3Now ∠BOC=90°  diagonals of square bisect each other at 90°⇒∠BOP+∠POC=90°⇒∠POC=90°-67
5°=22 5°  using 3i
 e ∠POC=2212°ii) To prove : ∠BDC=2∠POCSince ABCD is a squareAB∥CD and  and BD is a transversal∠CBD=∠BDA=45°  alternate interior anglesAlso, ∠ADC=90°  As ABCD is a square⇒∠BDA+∠BDC=90°⇒45°+∠BDC=90°⇒∠BDC=45°and ∠POC=22
5°So, ∠BDC=2 ∠POC=45°iii) Similarly try this part as a part of your practise
Regards

Q. In a square ABCD m diagonals meet at O. P is a point on BC, such that OB = BP. Show that : (i) ∠ P O C = 22 1 2 ° (ii) ∠ B D C = 2 ∠ P O C (iii) ∠ B O P = 3 ∠ C O P

Q. In a square ABCD m diagonals meet at O. P is a point on BC, such that OB = BP.
Show that :
(i) $∠ P O C = (22 \frac{1}{2}) °$
(ii) $∠ B D C = 2 ∠ P O C$
(iii) $∠ B O P = 3 ∠ C O P$