A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. - Mathematics

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Sum

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

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Solution


OP ⊥ AP

∴ ∠OPA = 90°  ...[Tangent at any point of a circle is perpendicular to the radius through the point of contact]

In ∆OAP,

OA2 = OP2 + PA2

⇒ 132 = 52 + PA2

⇒ PA = 12 cm

Now, perimeter of ∆ABC = AB + BC + CA

= AB + BR + RC + CA

= (AB + BR) + (RC + CA)

= (AB + BP) + (CQ + CA)  ...[∵ BR = BP, RC = CQ i.e., tangents from external point to a circle are equal]

= AP + AQ

= 2AP  ...[∵ AP = AQ]

= 2 × 12

= 24 cm

Hence, the perimeter of ∆ABC = 24 cm.

  Is there an error in this question or solution?
Chapter 9: Circles - Exercise 9.4 [Page 112]

APPEARS IN

NCERT Exemplar Mathematics Class 10
Chapter 9 Circles
Exercise 9.4 | Q 14 | Page 112
RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 24 | Page 35

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