Question

14. An isosceles triangle ABC is inscribed in a circk. If AB - AC - 13 cm and BC = 10cm, find the
radius of the circle

Answer 1

Answer:

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Answer 2

SOLUTION:-

Given:

•An isosceles ∆ABC, is inscribed in a circle.

•AB= AC= 13cm

•BC= 10cm

To find:

The radius of the circle.

Explanation:

AD perpendicular to BC

BD= DC=5cm

OA= OC= radius=r cm

USING PYTHAGORAS THEOREM:

$AD = \sqrt{ {AB}^{2} - {BD}^{2} } \\ \\ = > \sqrt{ {13}^{2} - {5}^{2} } \\ \\ = > \sqrt{169 - 25} \\ \\ = > \sqrt{144} \\ \\ = > AD = 12cm$

Therefore,

In ∆OCD,

OD = (12-r)cm

So,

=) OC² = OD² +CD²

=) r² = (12-r)² + 5²

=) r² = 12² + r² -2×12×r + 25

=) r² = 144 + r² - 24r +25

=) r² = r² -24r +169

=) 24r = 169

=) r= 169/24

=) r= 7.04cm

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