Question

# In a circle, O is the centre and ∠COD is a right angle. AC=BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

A

105 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

141.4 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

138.6 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

Can't be determined

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct options are A 105 cm B 141.4 cm C 138.6 cm D Can't be determined AO=BO ...1 [radius] CA=BD ...2 [given] Adding the equations 1 and 2: AO+AC=OB+BD ⇒OC=OD ⇒∠ODC=∠OCD Since, ∠COD=90∘ Therefore, ∠ODC=∠OCD=45∘ Now, join OP. OP is perpendicular to CD. [Line joining center to tangent at point of contact] tan∠ODP=OPPD ⇒tan45∘=100PD ⇒1=100PD ⇒PD=100 cm sin∠ODP=OPPD ⇒sin45∘=100OD ⇒OD=1000.7071 ⇒OD=141.42 cm BD=OD−OB ⇒BD=141.42–100 ⇒BD=41.42 cm ∴AC+CP=100+41.42=141.42 cm

Suggest Corrections
3
Join BYJU'S Learning Program
Select...
Related Videos
Theorems
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...