Question
AB and CD are parallel tangents to a circle with center O. Points P and Q are on AB and CD, respectively, such that PQ touches the circle at R. Find the measure of ∠ EOP.
Since PQ is tangent to the circle at R, PO bisects the angles at ∠ EOR. Thus, EOP = POR = θ 1 (let) QO bisects the angle at FOR. Thus, FOQ = QOR = θ ₂ (let) Since AB and CD are parallel tangents to the circle, EF must be a straight line. Thus, from the diagram, ∠ EOP + POR + FOQ + QOR = 180° 2 ( θ 1 + θ 2 ) = 180° ( θ 1 + θ 2 ) = 90° ∠ EOP = 90°More Geometry Questions
- O and C are the respectively orthocentre and circumcentre of ∆PQR. The line PO is extended which intersect line QR at S. such that, ∠QCR = 140°, ∠PQS = 58°...
- Angles of a triangle are in the ratio 2 : 3 : 7. Find the sum of the smallest and largest angle of the triangle.
- If the area of a regular hexagon is 384√3 cm2, then find the perimeter of the same hexagon.
- Find the area of triangle having sides in the ratio 4:5:7 & the perimeter of the triangle is 16 cm
- What will be inradius of a right angle triangle whose base is 11 cm & height is 60 cm ?
- ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12√5 and BC = 24 cm then radius of circle is
- If in a ΔABC, D is a point on BC such that BD = 5cm , BC = 9 cm then what is ratio of area of ΔABD to area of ΔADC ?
- In a circle, two chords of lengths p and q subtend the angles of 60° and 90° at the center respectively. Which of the following is correct in this scenario...
- Question 9
- Find the area of triangle having sides 7m, 8m, and 9m.
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
