In the given figure, PQ and PR are tangents to a circle with center Osuch that angle QPR =70°then angle OQR is equal to
Answers
Answer:
then angle OQR = 35
Step-by-step explanation:
QP=QR
Therefore angle Q = R
Therefore in triangle PQR,
Q + R + P = 180
Q + Q + 70 = 180
2Q = 110
Q = 55
angle PQR = 90
Therefore, angle PQR = angle OQR + angle RQP
therefore, 55 + angle OQR = 90
therefore, angle OQR = 35
Answer:
The required angle ∠OQR is 35°
Step-by-step explanation:
Explanation :
Given , PQ and PR tangents to a circle with centre O
∠QPR = 70 °
As we know tangent is perpendicular to radius at point of contact,
So, ∠ORP = ∠OQP = 90
Step1:
So , in quadrilateral PQOR
∠RPQ+∠PQO+∠QOR+∠ORP = 360 ° (sum of angle of a quadrilateral is 360)
70 +90+90+∠QOR = 360 (∠QPR = 70 °given ,∠ORP = ∠OQP = 90 )
⇒250 +∠QOR = 360
⇒∠QOR = 360-250= 110°
Step 2:
OQ = OR (radius of circle )
Therefore , ∠ORQ = ∠OQR
Let the angle of ∠ORP = ∠OQP be x .
In ΔQOR
∠QOR+∠ORP +∠OQP = 180 ° (Sum of angle of triangle os 180)
110 +x+x = 180 (where∠QOR is 110° )
⇒2x = 70
⇒ x = 35° = ∠OQR
Final answer :
Hence , the angle of ∠OQR is 35°
