In triangle abc ab=2cm ac=6cm and bc=2root7cm
a) use 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

c) calculate the area in cm^2 of the shaded region bcd

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.

step-by-step explanation:

x is variable or an unknown value to find

example:

2x = 5 which means x = 3