Share
Notifications

View all notifications
Advertisement

In the Given Figure, Mn is the Common Chord of Two Intersecting Circles and Ab is Their Common Tangent. Prove that the Line Nm Produced Bisects Ab at P. - Mathematics

Login
Create free account


      Forgot password?

Question

In the given figure, MN is the common chord of two intersecting circles and AB is their common tangent.

Prove that the line NM produced bisects AB at P.

Solution

From P, AP is the tangent and PMN is the secant for first circle.
∴ `AP^2 = PM × PN` …… (i)
Again from P, PB is the tangent and PMN is the secant for second circle.
∴ `PB^2 = PM × PN` ……..(ii)
From (i) and (ii)
`AP^2 =  PB^2`
⇒ AP = PB
Therefore, P is the midpoint of AB.

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (C) | Q: 14 | Page no. 285
Advertisement
In the Given Figure, Mn is the Common Chord of Two Intersecting Circles and Ab is Their Common Tangent. Prove that the Line Nm Produced Bisects Ab at P. Concept: Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection.
Advertisement
View in app×