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in triangle ABC AB=2cm AC=6cm and BC=2root7cm

Ause the cosine rule to show

the circle with centre A and radius 2cm intersects AC at point D

b)calculate the length in cm of the arc BD

Ccalculate the area in cm^2 of the shaded region BCD

Verified Answer :

OfficialPyrocynical

I drew a diagram and labeled some points. is the centre of the circle and D, E and F are points where the sides of the triangle are tangent to the circle. Thus angles CAB, PDB and BEP are right angles. Suppose the radius of the circle is r and the side length of CA is s. By the symmetry of the diagram E is the midpoint of BC. Notice also that the length of AD is r.

I used Pythagoras Theorem 3 times. Once for the triangle ABC to find the length of BC and hence BE in terms of s. A second for triangle BEP to find the length of BP, and a third time for triangle BPD to write an equation involving s and r. Solve for r.

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