ICSE Class 10CISCE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Tangent at P to the Circumcircle of Triangle Pqr is Drawn. If the Tangent is Parallel to Side, Qr Show that δPqr is Isosceles. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?
ConceptTangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments

Question

Tangent at P to the circumcircle of triangle PQR is drawn. If the tangent is parallel to side, QR show that ΔPQR is isosceles.

Solution

DE is the tangent to the circle at P.
DE ∥ QR (Given)

`∠`EPR  = `∠`PRQ (Alternate angles are equal)
`∠`DPQ = `∠`PQR (Alternate angles are equal) ….. (i)
Let `∠`DPQ = x and `∠`EPR = y
Since the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment

∴ `∠`DPQ = `∠`PRQ ……….. (ii) (DE is tangent and PQ is chord)
from (i) and (ii)
`∠` PQR  = `∠`PRQ
⇒ PQ = PR
Hence, triangle PQR is an isosceles triangle.

  Is there an error in this question or solution?

APPEARS IN

Solution Tangent at P to the Circumcircle of Triangle Pqr is Drawn. If the Tangent is Parallel to Side, Qr Show that δPqr is Isosceles. Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
S
View in app×