Question
ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ∠ADP = ∠BEQ = 100∘. What is value of ∠PRD?
Answer: Option C
:
C
Was this answer helpful ?
:
C
ADB is a straight line. By linear pair axiom,
∠ADP + ∠PDB = 180∘
100 + ∠PDB = 180∘
∠PDB = 80∘
Similarly ∠QED = 80∘
We have, ∠DPE = 90∘ (angle subtended by a diameter)
In △DPE,
∠DPE + ∠PED + ∠EDP = 180
[Angle sum property of a triangle]
∠PED = 10∘
Similarly ∠QDE = 10∘
In △DRE,
∠DRE + ∠RDE + ∠RED = 180
[Angle sum property of a triangle]
∠DRE = 160∘
PRE is a straight line. By linear pair axiom,
∠PRD + ∠DRE = 180∘
∠PRD + 160 = 180∘
∠PRD = 20∘
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution