Question

Given: Tangents
LA
and
LB

m∠AOB=110°
Find: m∠ALO.

Answer 1

m<ALO=35°

Explanation:

we know that

The right triangle AOL is congruent with the right triangle BOL

because

OA=OB=radius of the circle

OL is a common side

LA=LB ---> by applying the Pythagoras theorem

therefore

m<AOL=m<AOB/2

m<AOL=110°/2

m<AOL=55°

Remember that

m<AOL+m<ALO=90° ------> by complementary angles

m<ALO=90°-55°=35°