CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A triangle ABC is drawn to circumscribe a circle of radius 3cm , such that the segments BD and DC are respectively of lengths 6cm and 9cm . If the area of ΔABC is 54cm2 , find the lengths of sides AB and AC .

Open in App
Solution


Since BE and BD are tangents from same point, therefore BD=BE=6cm.

Similarly, CD=CF=9cm and AE=AF=xcm (say)

Now,

arΔABC=arΔAOB+arΔBOC+arΔAOC

54=12×OE×AB+12×OD×BC+12×OF×AC

54=12[3×(x+6)+3×(6+9)+3×(x+9)]

54=12×3×[(x+6)+(6+9)+(x+9)]

54=12×3×[2x+30]

54=3×[x+15]

18=x+15

x=3cm

Hence, AB=6+3=9cm and AC=9+3=12cm


flag
Suggest Corrections
thumbs-up
85
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Bulls Eye View of Geometry
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon