ABC is an isosceles triangle and AC, BC are the tangents at M and N resepectively. DE is the diameter of the circle. $∠ A D P = ∠ B E Q = 100^{\circ}$ . What is value of $∠ P R D$ ?

60^{\circ}

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50^{\circ}

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20^{\circ}

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C a n^{'} t b e d e t e r m i n e d

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Solution

The correct option is C $20^{\circ}$
$∠ P D B = ∠ Q E A = 80^{\circ} ∴ ∠ P E D = ∠ Q D E = 10^{\circ} (∵ ∠ D P E = ∠ D Q E = 90^{\circ}) ∴ ∠ D R E = 180 - (10 + 10) = 160^{\circ} ∴ ∠ P R D = 180 - ∠ D R E = 20^{\circ}$

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ABC is an isosceles triangle and AC, BC are the tangents at M and N resepectively. DE is the diameter of the circle. ∠ADP=∠BEQ=100∘. What is value of ∠PRD ?

The correct option is C 20∘∠PDB=∠QEA=80∘∴∠PED=∠QDE=10∘(∵∠DPE=∠DQE=90∘)∴∠DRE=180−(10+10)=160∘∴∠PRD=180−∠DRE=20∘

ABC is an isosceles triangle and AC, BC are the tangents at M and N resepectively. DE is the diameter of the circle. $∠ A D P = ∠ B E Q = 100^{\circ}$ . What is value of $∠ P R D$ ?

The correct option is C $20^{\circ}$
$∠ P D B = ∠ Q E A = 80^{\circ} ∴ ∠ P E D = ∠ Q D E = 10^{\circ} (∵ ∠ D P E = ∠ D Q E = 90^{\circ}) ∴ ∠ D R E = 180 - (10 + 10) = 160^{\circ} ∴ ∠ P R D = 180 - ∠ D R E = 20^{\circ}$