Question

In the given figure, $△ A BC$ circumscribes a circle. If $A R = 3$ cm, $BP = 4$ cm and $QC = 5$ cm, find the perimeter of $△ A BC$ .

Approach

Using the property that tangents from an external point are equal, $BP = BR = 4$ cm, $CQ = CP = 5$ cm, $A R = A Q = 3$ cm. Perimeter $= A B + BC + A C = 7 + 9 + 8 = 24$ cm.

Step-by-step working

1
Tangents from external point: $BP = BR = 4$ cm, $CQ = CP = 5$ cm, $A R = A Q = 3$ cm
1 mark
2
Perimeter $= A B + BC + A C = 7 + 9 + 8$
0.5 marks
3
$= 24$ cm
0.5 marks

Concepts used

tangentscircleperimeter

Approach

Step-by-step working

Concepts used

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