Question

In the given figure, AB is perpendicular to AD and BC. Also ∠C = 40°, ∠D = 30°. Which is longer AO or BO?

Answer 1

Given:

AB is perpendicular to AD and BC.

∠C = 40°.

∠D = 30°.

Figure shows quadrilateral ABCD with diagonals intersecting at O.

Stepwise calculation:

1. Since AB ⊥ AD and AB ⊥ BC, triangles ABO and ADO and triangles BCO and BDO involve right angles at B and A respectively.
2. With ∠C = 40° and ∠D = 30°, the intersecting diagonals form angles around point O.
3. Using angle properties at intersection O of diagonals and perpendicularities, one can infer the measures of angles in triangles ABO and BCO.
4. Using the property that in a triangle, greater angle lies opposite longer side and vice versa, compare length AO in triangle AOD and BO in triangle BOC.
5. From the given angles, it can be deduced that AO > BO.

AO is longer than BO.