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Mathematics · Circles · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

Mathematics · Chapter 10 · NCERT Examples

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NCERT Example

Example 1

concentric circles · perpendicular chord theorem

Prove that in two concentric circles, a chord of the larger circle that touches the smaller circle is bisected at the point of contact.

Two concentric circles with chord AB of the larger circle tangent to the smaller circle at P.
Figure 10-8 from the supplied NCERT chapter.

Solution

Board-exam working:

Let the two circles have common centre O. Chord AB of the larger circle touches the smaller circle at P.

Join OP.

Since AB is tangent to the smaller circle at P, its radius OP is perpendicular to AB.

OP⊥ABOP\perp AB

AB is also a chord of the larger circle. The perpendicular from the centre of a circle to a chord bisects the chord.

AP=PBAP=PB

Final answer

Hence, the chord AB is bisected at P.