Question

In a Triangle AB=AC, <BAC=120°. D is the middle point of BC. O circle is drawn inside the triangle which touches AD,CD,& AC. If OA=4(meter) What's the radius of the circle???

Answer 1

81523, Math / Geometry/ Completed

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Solution.

AD is the median, height and bisector, because $\Delta ABC$ is an isosceles.

AD $\perp$ BC, $\angle BAD = \angle DAC = 60{}^{\circ}$ . $\Delta$ ADC - rectangular. O - center of the inscribed circle. The center of the inscribed circle lies on the bisectors of the angles of the triangle. AO-bisector. $\angle$ EAO= $\angle OAC = 30{}^{\circ}$ . OE is the radius of the inscribed circle. OE $\perp$ AD. $\Delta$ AOE- rectangular triangle. AE=AO*sin30o=2m

Answer: $R = 2m$

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