ABCD is a quadrilateral. From any point P on AB a line drawn parallel to BC meets AC at Q and the line through Q drawn parallel to CD meets AD at R. Prove that QR || AD.
Tangent to a circle is a straight line which touches the circle at only one point and the point of contact is perpendicular to the radius drawn from the center of the circle.
In the given question
Line segment PQ is radius, Line segment QR is is a tangent to the circle(P) at point Q.
Here QR is perpendicular to PQ because tangent to a circle is perpendicular to the point of contact and a line (PQ) drawn from the center of the circle (P).
∴ ∠PQR = 90° given ∠QPR = 53° We have to find ∠QRP .
We know the sum of all the interior angles in a triangle is = 180°
Answers & Comments
Answer:The measure of angle ∠QRP = 37°.
What is a tangent to a circle ?
Tangent to a circle is a straight line which touches the circle at only one point and the point of contact is perpendicular to the radius drawn from the center of the circle.
In the given question
Line segment PQ is radius, Line segment QR is is a tangent to the circle(P) at point Q.
Here QR is perpendicular to PQ because tangent to a circle is perpendicular to the point of contact and a line (PQ) drawn from the center of the circle (P).
∴ ∠PQR = 90° given ∠QPR = 53° We have to find ∠QRP .
We know the sum of all the interior angles in a triangle is = 180°
∠PQR + ∠QPR + ∠QRP = 180°
90° + 53° + ∠QRP = 180°
∠QRP = 180° - (90° + 53°)
∠QRP = 180° - 143°
∠QRP = 37°
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