Question

In the given figure, AD and AE are the tangents to a circle with centre O and BC touches the circle at F. If AE = 5 cm then perimeter of ΔABC is ______.

Options

• 15 cm

• 10 cm

• 22.5 cm

• 20 cm

Answer 1

In the given figure, AD and AE are the tangents to a circle with centre O and BC touches the circle at F. If AE = 5 cm then perimeter of ΔABC is 10 cm.

Explanation:

Let the tangent BC touch the circle at F. Using the standard tangent-length facts (tangents from the same external point are equal) one gets, after splitting BC at F and regrouping the segments, that

Perimeter(ΔABC) = AB + BC + CA

= AE + AD

= 2·AE

Since AE = 5 cm, perimeter = 2 × 5 = 10 cm.