In the fig PQ=16cm, OQ=10 cm find area(triangle OPQ) - Maths - Areas Related to Circles

Question

In the fig PQ=16cm, OQ=10 cm find area(triangle OPQ)

Neha Sethi · Accepted Answer

Dear student
Given : PQ=16 cm, OQ=10 cmTo find : area △OPQSolution: Here OM⊥PQand we know that ⊥ from the centre to a chord bisects the chord
SoPQ=2 MQ⇒16=2 MQ⇒MQ=8 cmSo, MQ=PM=8 cm Consider, △OMQBy pythagoras theorem we haveOQ2=OM2+MQ2⇒102=OM2+82⇒OM2=100-64⇒OM=6 cmNow area of △OPQ=area of △OPM+area of △OMQ=12×PM×OM+12×MQ×OM   as area of right triangle=12×Base×Height=12×OMPM+MQ=12×OM×PQ=12×6×16=48 cm2
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In the fig. PQ=16cm, OQ=10 cm find area(triangle OPQ)