NCERT Exemplar Solutions Class 10 Mathematics Solutions for Circles - Exercise 9.4 in Chapter 9 - Circles
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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 circle at P and Q. If a tangent BC is drawn at point R lying on minor arc PQ to intersect AP at B and AQ at C. Find the perimeter of ΔABC.
OA = 13 cm
OP = OQ = 5 cm
OP and PA are radius and tangent respectively at contact point P.
∴ ∠OPA = 90°
In right angled ΔOPA by Pythagoras theorem
PA2=OA2–OP2=132–52=169–25=144
⇒ PA = 12 cm
Points A, B and C are
exterior to the circle and tangents drawn from an external point to a circle
are equal so
PA=QA
BP=BR
CR=CQ
Perimeter of ΔABC
= AB + BC + AC
= AB + BR + RC + AC ......... [From figure]
= AB+BP+CQ+AC=AP+AQ
= AP + AP
= 2AP
= 2 × 12
= 24 cm
So, the perimeter of ΔABC = 24 cm.
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